On Duclos-Exner's conjecture about waveguides in strong uniform magnetic fields

TL;DR

This paper investigates the spectral properties of a Dirichlet Laplacian with a uniform magnetic field on curved strips, providing conditions for the existence of discrete spectrum in strong magnetic fields.

Contribution

It establishes a sufficient condition for the discrete spectrum to exist in the strong magnetic field limit for curved waveguides.

Findings

Discrete spectrum exists under certain geometric conditions.

Strong magnetic fields influence spectral properties significantly.

Results support Duclos-Exner's conjecture on waveguides.

Abstract

We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition ensuring the existence of the discrete spectrum in the strong magnetic field limit.