Motivated by models of anyonic systems, we investigate the self-adjointness and spectral properties of two-dimensional Schrödinger operators for one non-relativistic particle in presence of Aharonov-Bohm (AB) fluxes. We start by addressing the simple case of a single infinite realistic solenoid, i.e., with a AB flux perturbed by a regular magnetic field, and study the properties of the operator by means of quadratic form techniques. Next, we apply the obtained results to the case of many ideal fluxes on the plane. Finally, we present some work in progress about the homogenization regime where the number of fluxes goes to infinity, while the single flux intensity tends to zero in such a way that the total flux remains finite.
Joint work with Davide Fermi (Politecnico di Milano).
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