Speaker
Davide Fermi, Politecnico di Milano
Abstract
It is well-known that anyonic Hamiltonians can be represented, in a suitable gauge, as a magnetic Schrödinger operators with singular vector potentials of Aharonov-Bohm type. In this context, even self-adjointness becomes a non-trivial issue. We present several approaches to classify all self-adjoint realizations of the two-body anyonic Hamiltonian, matching those for a charged particle which interacts with an ideal solenoid. We discuss the interpretation of these realizations in terms of zero-range interactions, emerging from resonances of systems with smooth electromagnetic fields in appropriate low-energy regimes. Next, we extend our analysis to a broader class of singular Hamiltonians, including Pauli and Dirac operators with one Aharonov-Bohm flux, as well as Schrödinger operators with multiple fluxes. We examine the associated self-adjoint extensions, along with their spectral and scattering features, and explore the connections with anyonic Hamiltonians.
This talk is based on joint works with William Borrelli, Domenico Cafiero and Michele Correggi (Politecnico di Milano).