The Flea on the Magnetic Elephant
Mathematical Physics
2025-05-20 v1 math.MP
Spectral Theory
Abstract
We investigate a two-dimensional magnetic Laplacian with two radially symmetric magnetic wells. Its spectral properties are determined by the tunneling between them. If the tunneling is weak and the wells are mirror symmetric, the two lowest eigenfunctions are localized in both wells being distributed roughly equally. In this note we show that an exponentially small symmetry violation can in this situation have a dramatic effect, making each of the eigenfunctions localized dominantly in one well only. This is reminiscent of the `flea on the elephant' effect for Schr\"odinger operators; our result shows that it has a purely magnetic counterpart.
Cite
@article{arxiv.2505.12846,
title = {The Flea on the Magnetic Elephant},
author = {Pavel Exner and Léo Morin},
journal= {arXiv preprint arXiv:2505.12846},
year = {2025}
}