Kumar, N
(1986)
*Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach.*
In: Pramana, 27
(1-2).
pp. 33-42.

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## Abstract

It is now well known that in 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 re-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 dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. 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 fiekl. We find a cross-over from the exponential to the power-low 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: | Journal Article |
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Publication: | Pramana |

Publisher: | Indian Academy of Sciences |

Additional Information: | Copyright of this article belongs to Indian Academy of Sciences. |

Keywords: | Quantum-ohmic resistance;disordered conductors;invariant imbedding;finite electric field;mobility edge. |

Department/Centre: | Division of Physical & Mathematical Sciences > Physics |

Date Deposited: | 11 Feb 2010 09:24 |

Last Modified: | 19 Sep 2010 05:35 |

URI: | http://eprints.iisc.ac.in/id/eprint/20906 |

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