Related Experiment Video
Updated: Mar 3, 2026

The Ingestion of Fluorescent, Magnetic Nanoparticles for Determining Fluid-uptake Abilities in Insects
Published on: December 20, 2017
The flea on the Magnetic Elephant
Pavel Exner1,2, Léo Morin3
1Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague, Czechia.
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.
Related Concept Videos
Other Unique Bacteria
Magnetic Fields
A magnetic field is defined by the force that a charged particle experiences...
Magnetic Force
The magnetic force acting on a moving charge...
Electric Charges
The English physicist William Gilbert studied the phenomenon of static electricity in...
Magnetic Flux
Suppose a surface is divided into elements of area dA. For each element, the component of the magnetic field that is normal to the...
Magnetic Moment of an Electron

