Remarks on Regular Approximations to the Robin Aharonov-Bohm Hamiltonian

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 $\Gamma$-convergence technique, and they hold for the more general setting of smooth, closed and compact surfaces and continuous and bounded magnetic potentials.

Mathematical Physics (math-ph); Spectral Theory (math.SP); Quantum Physics (quant-ph)

arXiv:2608.00637 [math-ph]

(or arXiv:2608.00637v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2608.00637 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1142/S0129055X26500157 Focus to learn more DOI(s) linking to related resources

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