English

Magnetic Dirichlet Laplacian in curved waveguides

Spectral Theory 2025-03-03 v1 Functional Analysis

Abstract

For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable. Any perturbation of the straight strip produces eigenvalues below the essential spectrum. In this paper, a magnetic field is added. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small but non-local deformations of the waveguide.

Keywords

Cite

@article{arxiv.2502.21247,
  title  = {Magnetic Dirichlet Laplacian in curved waveguides},
  author = {Diana Barseghyan and Swanhild Bernstein and Baruch Schneider and Martha Lina Zimmermann},
  journal= {arXiv preprint arXiv:2502.21247},
  year   = {2025}
}