Related papers: Analytic toolkit for the Anderson model with arbitrary disorder

Analytic toolkit for the Anderson model with arbitrary disorder

URL: http://arxiv.org/abs/2507.06903v2
Date: Tue, 15 Jul 2025 02:18:39 GMT
Title: Analytic toolkit for the Anderson model with arbitrary disorder
Authors: Oleg Evnin,
Abstract summary: The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials.<n>Supersymmetry-based techniques are employed to give an explicit linear integral equation whose solutions control the density-of-states.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous developments in various branches of physics. The literature is silent, however, on practical analytic tools for computing the density-of-states of this model when the distribution of the on-site potentials is arbitrary. Here, supersymmetry-based techniques are employed to give an explicit linear integral equation whose solutions control the density-of-states. The output of this analytic procedure is in perfect agreement with numerical sampling. By Thouless formula, these results immediately provide analytic control over the localization length.

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