2026/07/28 by Cesar R. De Oliveira, César R. de Oliveira, Cesar R. de Oliveira
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35J10 #msc:47A55 #msc:81Q10. #msc:81Q15 #quant-ph
paper · pdf · doi:10.1142/s0129055x26500157
Accepted in Reviews in Mathematical Physics
arxiv created 2026/08/01 · arxiv updated 2026/08/04
In the space \mathbb R3, 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.