arXiv subjects

Khaled Abou Alfa

Publications and source records attributed to Khaled Abou Alfa.

2 recordsLinked to original sources

arXiv2023

Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions

This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the variable magnetic field (involving a localization of the eigenfunctions near the boundary), we establish a semiclassical expansion of the lowest eigenvalues. In particular, we prove that the eigenvalues become simple in the semiclassical limit.

math.SP↗

arXiv2022

Tunneling effect in two dimensions with vanishing magnetic fields

In this paper, we consider the semiclassical 2D magnetic Schr{ö}dinger operator in the case where the magnetic field vanishes along a smooth closed curve. Assuming that this curve has an axis of symmetry, we prove that semi-classical tunneling occurs. The main result is an expression the splitting of the first two eigenvalues and an explicit tunneling formula.

math-ph↗