TY  - JOUR
ID  - Barseghyan2025
LB  - Barseghyan2025
AU  - Barseghyan, Diana
AU  - Bernstein, Swanhild
AU  - Schneider, Baruch
AU  - Zimmermann, Martha Lina
TI  - Magnetic Dirichlet Laplacian in curved waveguides
ST  - Magnetic Dirichlet Laplacian in curved waveguides
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 3
SP  - 293
EP  - 305
DO  - https://doi.org/10.7494/OpMath.2025.45.3.293
UR  - https://doi.org/10.7494/OpMath.2025.45.3.293
AB  - For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable with respect to waveguide deformations. This means that if the waveguide is a straight strip then the spectrum of the Dirichlet Laplacian is purely essential. From the other hand, the perturbation of the straight strip produces eigenvalues below the essential spectrum. In this paper, the Dirichlet-Laplace operator with a magnetic field is considered. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small but non-local deformations of the waveguide.
KW  - magnetic Schrödinger operators
KW  - essential spectrum
KW  - discrete spectrum
SN  - 1232-9274
ER  -