Exponential scaling limit of the single-particle Anderson model via adaptive feedback scaling

TL;DR

This paper reformulates the bootstrap Multi-Scale Analysis to explicitly demonstrate exponential decay of eigenfunctions and correlators in Anderson models, extending results to certain marginal disorder distributions.

Contribution

It introduces an explicit reformulation of BMSA that clarifies its implications for exponential decay and extends the exponential scaling limit to broader disorder distributions.

Findings

BMSA implies asymptotic exponential decay of eigenfunctions and correlators.

The exponential scaling limit holds for a class of marginal distributions with low regularity.

The reformulation makes the decay implications of BMSA more explicit.

Abstract

We propose a reformulation of the bootstrap version of the Multi-Scale Analysis (BMSA), developed by Germinet and Klein, to make explicit the fact that BMSA implies asymptotically exponential decay of eigenfunctions (EFs) and of EF correlators (EFCs), in the lattice Anderson models with diagonal disorder, viz. with an IID random potential. We also show that the exponential scaling limit of EFs and EFCs holds true for a class of marginal distributions of the random potential with regularity lower than H\"older continuity of any positive order.