5 papers
Semiclassical resonances under local magnetic fields
Pavel Exner, Ayman Kachmar
We study resonances for the semiclassical magnetic Laplacian in the full plane with a compactly supported magnetic field in the framework of semiclassical complex scaling and black…
Isoperimetric inequalities for the lowest magnetic Steklov eigenvalue
Ayman Kachmar, Vladimir Lotoreichik
This paper studies the optimization of the lowest eigenvalue of the magnetic Steklov problem on planar domains. In the bounded domain setting and for magnetic fields of moderate st…
Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk
Bernard Helffer, Ayman Kachmar, François Nicoleau
We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field li…
Isoperimetric inequality with zero magnetic field in doubly connected domains
Mrityunjoy Ghosh, Ayman Kachmar
We investigate how the lowest eigenvalue of a magnetic Laplacian depends on the geometry of a planar domain with a disk shaped hole, where the magnetic field is generated by a sing…
Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains
Bernard Helffer, Ayman Kachmar, Francois Nicoleau
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operato…