# Absence of embedded eigenvalues for translationally invariant magnetic Laplacians

## TL;DR

This paper proves that certain two-dimensional magnetic Laplacians with translational symmetry do not have embedded eigenvalues, using an improved harmonic approximation method under various magnetic field conditions.

## Contribution

It introduces an enhanced harmonic approximation technique to demonstrate the absence of embedded eigenvalues in translationally invariant magnetic Laplacians.

## Key findings

- No embedded eigenvalues under specified magnetic field conditions
- Improved harmonic approximation method developed
- Results applicable to a range of magnetic field behaviors

## Abstract

Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum under various assumptions on the behavior of the magnetic field.