The flea on the Magnetic Elephant
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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Letters in Mathematical Physics
- Volume
- 116
- Issue
- 2
- Pages
- 23–23
- Publication date
- 27 February 2026
- Language
- EN