Remarks on Regular Approximations to the Robin Aharonov-Bohm Hamiltonian

• URL: http://arxiv.org/abs/2608.00637v1
• Date: Sat, 01 Aug 2026 12:46:48 GMT
• Title: Remarks on Regular Approximations to the Robin Aharonov-Bohm Hamiltonian
• Abstract summary: It is shown that approximations via smooth potentials and then a barrier in the solenoid interior give Dirichlet boundary conditions.<n>The approximations are in the strong resolvent sense and obtained through the $$-convergence technique.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the space $\mathbb R^3$, for Robin parameter $L>0$, it is shown that there is a family of Schrödinger 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 $Γ$-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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