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Abstract: The Landauer scattering approach to 4-probe resistance is revisited for thecase of a d-dimensional disordered resistor in the presence of decoherence. Ourtreatment is based on an invariant-embedding equation for the evolution of thecoherent reflection amplitude coefficient in the length of a 1-dimensionaldisordered conductor, where decoherence is introduced at par with the disorderthrough an outcoupling, or stochastic absorption, of the wave amplitude intoside transverse channels, and its subsequent incoherent re-injection into theconductor. This is essentially in the spirit of B{\-u}ttiker-sreservoir-induced decoherence. The resulting evolution equation for theprobability density of the 4-probe resistance in the presence of decoherence isthen generalised from the 1-dimensional to the d-dimensional case following ananisotropic Migdal-Kadanoff-type procedure and analysed. The anisotropy, namelythat the disorder evolves in one arbitrarily chosen direction only, is the mainapproximation here that makes the analytical treatment possible. Aqualitatively new result is that arbitrarily small decoherence reduces thelocalisation-delocalisation transition to a crossover making resistance momentsof all orders finite.

Author: Dibyendu Roy, N. Kumar


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