Speaker
Domenico Cafiero, Politecnico di Milano
Abstract
We consider a non-relativistic quantum particle in \(\mathbb{R}^2\) in presence of several Aharonov-Bohm fluxes. We investigate the so-called homogenization limit, making reference to a scaling regime where the intensities of the single fluxes and the distances between them go to zero as the number of fluxes grows, while the total flux remains finite. We show that the Friedrichs Hamiltonian converges (in the sense of \Gamma-convergence of quadratic forms) to a Schrödinger operator with a regular magnetic potential and Dirichlet boundary conditions defined outside the region were the fluxes are placed. Consequently, we obtain the strong resolvent convergence of the corresponding operators. Finally, we outline the case of many regularized Aharonov-Bohm potentials.
Based on a joint work with Michele Correggi and Davide Fermi (Politecnico di Milano).