2025/07/09 by Oleg Evnin, Evnin, Oleg · 3 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2507.06903
openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 does not readily provide, however, 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.