Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole

Laura Abatangelo; Veronica Felli

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arXiv · 2410.23917

Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole

Laura Abatangelo·Veronica Felli

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Abstract

We study double eigenvalues of Aharonov-Bohm operators with Dirichlet boundary conditions in planar domains containing the origin. We focus on the behavior of double eigenvalues when the potential's circulation is a fixed half-integer number and the operator's pole is moving on straight lines in a neighborhood of the origin. We prove that bifurcation occurs if the pole is moving along straight lines in a certain number of cones with positive measure. More precise information is given for symmetric domains; in particular, in the special case of the disk, any eigenvalue is double if the pole is located at the centre, but there exists a whole neighborhood where it bifurcates into two distinct branches.

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Laura Abatangelo, Veronica Felli. 2024-10-31. Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole. https://arxiv.org/abs/2410.23917

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