# Lifshits tails for randomly twisted quantum waveguides

## TL;DR

This paper investigates the asymptotic behavior of the integrated density of states for a 3D quantum waveguide with random twisting, revealing how the Lifshits tail depends on the decay rate of the twisting at infinity.

## Contribution

It introduces the Lifshits tail analysis for the IDOS of randomly twisted waveguides and explores the influence of twisting decay on Lifshits exponents.

## Key findings

- Lifshits tails are characterized for the IDOS in twisted waveguides.
- The Lifshits exponent depends on the decay rate of the twisting.
- Asymptotic behavior of the IDOS near the spectrum's infimum is established.

## Abstract

We consider the Dirichlet Laplacian $H_\gamma$ on a 3D twisted waveguide with random Anderson-type twisting $\gamma$. We introduce the integrated density of states $N_\gamma$ for the operator $H_\gamma$, and investigate the Lifshits tails of $N_\gamma$, i.e. the asymptotic behavior of $N_\gamma(E)$ as $E \downarrow \inf {\rm supp}\, dN_\gamma$. In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.