On the semiclassical Laplacian with magnetic field having self-intersecting zero set

On the semiclassical 3D Neumann Laplacian with variable magnetic field

From the Laplacian with variable magnetic field to the electric Laplacian in the semiclassical limit

We consider a twisted magnetic Laplacian with Neumann condition on a smooth and bounded domain of R2 in the semiclassical limit h → 0. Under generic assumptions, we prove that the eigenvalues admit a complete asymptotic expansion in powers of h1/4.

On the Semiclassical Magnetic Laplacian and Connected Topics

The aim of this course is to introduce the reader to the general techniques appearing in the spectral theory of the semiclassical magnetic Laplacian. We explain how we can construct quasi-eigenpairs and how the investigation of the magnetic Laplacian can be reduced to the one of model operators. In particular, the localization estimates of Agmon and the Born-Oppenheimer approximation are discus...

Semiclassical 3D Neumann Laplacian with variable magnetic field: a toy model

In this paper we investigate the semiclassical behavior of the lowest eigenvalues of a model Schrödinger operator with variable magnetic field. This work aims at proving an accurate asymptotic expansion for these eigenvalues, the corresponding upper bound being already proved in the general case. The present work also aims at establishing localization estimates for the attached eigenfunctions. ...

Measurement of the Earth’s Magnetic Field Vector based on zero field finding algorithm using optically pumped magnetometers

Atomic magnetometers have found widespread applications in precise measurement of the Earth’s magnetic field due to their high sensitivity. In these measurements, various methods have been utilized to compensate the Earth’s magnetic field in an unshielded environment. In this paper, we have proposed a method based on finding the minimum resonance frequency (corresponding to minimum magnetic fie...