Ballistic Transport for Schr\"odinger Operators with Quasi-periodic Potentials

TL;DR

This paper proves that Schr"odinger operators with generic quasi-periodic potentials exhibit ballistic transport in dimensions greater than one, advancing understanding of quantum dynamics in complex potentials.

Contribution

It establishes the existence of ballistic transport for a broad class of quasi-periodic Schr"odinger operators in higher dimensions, a significant theoretical development.

Findings

Ballistic transport proven for generic quasi-periodic potentials

Results apply to any dimension greater than one

Advances understanding of quantum transport phenomena

Abstract

We prove the existence of ballistic transport for a Schr\"odinger operator with a generic quasi-periodic potential in any dimension $d>1$.