# A geometric Iwatsuka type effect in quantum layers

## TL;DR

This paper investigates how geometric modifications to quantum layers influence magnetic transport, showing conditions under which the spectrum becomes absolutely continuous, enabling particle movement in a magnetic field.

## Contribution

It introduces new conditions for magnetic transport in quantum layers with geometric perturbations, extending understanding of spectral properties in such systems.

## Key findings

- Geometric perturbations can induce absolutely continuous spectrum.
- Conditions for magnetic transport depend on layer geometry.
- Spectrum can transition from degenerate to absolutely continuous.

## Abstract

We study motion of a charged particle confined to Dirichlet layer of a fixed width placed into a homogeneous magnetic field. If the layer is planar and the field is perpendicular to it the spectrum consists of infinitely degenerate eigenvalues. We consider translationally invariant geometric perturbations and derive several sufficient conditions under which a magnetic transport is possible, that is, the spectrum, in its entirety or a part of it, becomes absolutely continuous.