Non-Perturbative Localization with Quasiperiodic Potential in Continuous Time

TL;DR

This paper proves Anderson localization for continuous one-dimensional quasiperiodic Schrödinger operators with analytic potentials, positive Lyapunov exponents, and typical phases and frequencies, advancing understanding of localization phenomena.

Contribution

It establishes non-perturbative localization results for a broad class of continuous quasiperiodic Schrödinger operators, extending previous discrete and perturbative findings.

Findings

Localization holds for almost all phases and Diophantine frequencies.

Positive Lyapunov exponent regime guarantees Anderson localization.

Results apply to analytic potentials in continuous models.

Abstract

We consider continuous one-dimensional multifrequency Schr\"odinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine frequencies.