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The Flea on the Magnetic Elephant

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arxiv 2505.12846 v1 pith:OZ657HRU submitted 2025-05-19 math-ph math.MPmath.SP

Pavel Exner , Léo Morin This is my paper
classification math-phmath.MPmath.SP
keywords magneticwellseffecteigenfunctionselephantflealocalizedsymmetric
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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.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Magnetic Double-Wells: Absence of Tunneling

    math-ph 2025-09 conditional novelty 8.0 of 10

    Placing four exponentially small potential bumps at a tunable height around a radial well makes the magnetic double-well hopping coefficient vanish, so the eigenvalue splitting is exactly zero.

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