# Lifshits Tails for Squared Potentials

## TL;DR

This paper studies the spectral properties of Schrödinger operators with squared alloy-type potentials, establishing Lifshits tail behavior in their integrated density of states, motivated by applications to randomly twisted waveguides.

## Contribution

It provides the first analysis of Lifshits tails for Schrödinger operators with squared alloy-type potentials, expanding understanding of spectral behavior in such models.

## Key findings

- Proved Lifshits tail asymptotics for the integrated density of states.
- Analyzed spectral properties of squared alloy-type potentials.
- Connected results to applications in randomly twisted waveguides.

## Abstract

We consider Schr\"odinger operators with a random potential which is the square of an alloy-type potential. We investigate their integrated density of states and prove Lifshits tails. Our interest in this type of models is triggered by an investigation of randomly twisted waveguides.