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arXiv · 2608.00637

Remarks on Regular Approximations to the Robin Aharonov-Bohm Hamiltonian

Cesar R. de Oliveira
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Abstract

In the space $\mathbb R^3$, for Robin parameter $L>0$, it is shown that there is a family of Schr\"odinger operators with penetrable toroidal solenoid and variable conductivity that approximates the magnetic Aharonov-Bohm operator with a Robin boundary condition at the solenoid (border). It is also shown that approximations via smooth potentials and then a barrier in the solenoid interior give Dirichlet boundary conditions. The approximations are in the strong resolvent sense and obtained through the $\Gamma$-convergence technique, and they hold for the more general setting of smooth, closed and compact surfaces and continuous and bounded magnetic potentials.

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Cesar R. de Oliveira. 2026-08-01. Remarks on Regular Approximations to the Robin Aharonov-Bohm Hamiltonian. https://doi.org/10.1142/s0129055x26500157

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