The superadiabatic projectors method applied to the spectral theory of magnetic operators

TL;DR

This paper generalizes the superadiabatic projectors method and applies it to spectral theory, improving understanding of the semiclassical magnetic Laplacian with potential applications in quantum physics.

Contribution

It extends the superadiabatic projectors method to a broader framework and applies it to spectral analysis of magnetic operators, enhancing previous results.

Findings

Generalized superadiabatic projectors for spectral theory

Improved semiclassical magnetic Laplacian results

Applicable to broader classes of magnetic operators

Abstract

This article deals with a generalization of the superadiabatic projectors method. In a general framework, the well-known superadiabatic projectors are constructed and accurately described in the case of rank one, when a remarkable factorization occurs. We apply these ideas to spectral theory and we explain how our abstract results allow to recover or improve recent results about the semiclassical magnetic Laplacian.