Absolute continuity of the spectrum of a Schrodinger operator with a potential which is periodic in some directions and decays in others

TL;DR

This paper proves that Schrödinger operators with mixed periodic and rapidly decaying potentials have purely absolutely continuous spectra, advancing understanding of spectral properties in mixed potential environments.

Contribution

It establishes the absolute continuity of the spectrum for Schrödinger operators with potentials that are periodic in some directions and decay super-exponentially in others, a novel spectral analysis result.

Findings

Spectrum is purely absolutely continuous.

Applicable to operators with mixed periodic and decaying potentials.

Enhances spectral theory for complex potential structures.

Abstract

We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.