Decohering $d$-dimensional quantum resistance
Dibyendu Roy and N. Kumar

The Landauer scattering approach to 4-probe resistance is revisited for the case of a d-dimensional disordered resistor $in~ the~ presence~ of~ decoherence$. Our treatment is based on an invariant-embedding equation for the evolution of the coherent reflection amplitude coefficient in the length of a 1-dimensional disordered conductor, where decoherence is introduced $at~ par$ with the disorder through an outcoupling, or stochastic absorption, of the wave amplitude into side (transverse) channels, and its subsequent incoherent re-injection into the conductor. This is essentially in the spirit of B{\"u}ttiker's reservoir-induced decoherence. The resulting evolution equation for the probability density of the 4-probe resistance in the presence of decoherence is then generalised from the 1-dimensional to the d-dimensional case following an anisotropic Migdal-Kadanoff-type procedure and analysed. The anisotropy, namely that the disorder evolves in one arbitrarily chosen direction only, is the main approximation here that makes the analytical treatment possible. A qualitatively new result is that arbitrarily small decoherence reduces the localisation-delocalisation transition to a crossover making resistance moments of all orders finite.

© 2008 The American Physical Society.