Work

The flea on the Magnetic Elephant

Year: 2026

Type: article

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 Schrödinger operators; our result shows that it has a purely magnetic counterpart.

Source: Letters in Mathematical Physics

DOI: 10.1007/s11005-026-02055-x

Authors: Pavel Exner, Léo Morin

Institutions: Czech Academy of Sciences, Nuclear Physics Institute, Czech Technical University in Prague, University of Copenhagen

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: European Commission, European Research Council, H2020 Marie Skłodowska-Curie Actions