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Quantum Transport in Mesoscopic SystemsComplexity and Statistical Fluctuations. A Maximum Entropy Viewpoint$
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Pier A. Mello and Narendra Kumar

Print publication date: 2004

Print ISBN-13: 9780198525820

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525820.001.0001

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ELECTRONIC TRANSPORT THROUGH QUASI-ONE-DIMENSIONAL DISORDERED SYSTEMS

ELECTRONIC TRANSPORT THROUGH QUASI-ONE-DIMENSIONAL DISORDERED SYSTEMS

Chapter:
(p.279) 7 ELECTRONIC TRANSPORT THROUGH QUASI-ONE-DIMENSIONAL DISORDERED SYSTEMS
Source:
Quantum Transport in Mesoscopic Systems
Author(s):

Pier A. Mello

Narendra Kumar

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525820.003.0007

This chapter treats the problem of finding the probability distribution of quantities related to quantum transport through a strictly one-dimensional (i.e., 1-channel) and through an N-channel quasi-one-dimensional disordered system. It uses the maximum entropy approach wherein the distribution for the random transfer matrix for an elementary building block is determined by maximizing the associated Shannon entropy, subject to the physically relevant constraints of flux conservation, time-reversal symmetry (when relevant), and the Ohmic small length-scale limit. The contents of this chapter include ensemble of transfer matrices; universality classes — the orthogonal and the unitary classes; invariant measure; the Fokker-Planck equation for a disordered one-dimensional conductor; the maximum-entropy ansatz for the building block; construction of the probability density for a system of finite length; the Fokker-Planck equation for a quasi-one-dimensional multi-channel disordered conductor; the diffusion equation for the orthogonal universality class, β = 1; the diffusion equation for the unitary universality class, β = 2; and universal conductance fluctuations in the good-metallic limit.

Keywords:   quasi-one-dimensional, disordered conductor, N-channel conductor, maximum entropy approach, Shannon's entropy, transfer matrix, universal conductance fluctuation, diffusion equation, moments, correlations

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