9 dec 2020 -- 17:00   [open in google calendar]

MS Teams Platform

Please write an e-mail to andrea.malchiodi@sns.it if you are interested in attending

Abstract.

In a pioneering work dating back to 1976, Leinaas and Myrheim foregrounded the possibility of two-dimensional systems of identical particles obeying fractional statistics (neither bosonic nor fermionic). This theoretical construct is nowadays believed to play a key role in the description of quasi-particles with fractional charges arising in the so-called fractional quantum Hall effect. In this seminar we discuss the effects of magnetic perturbations for a system of two anyons moving in a plane. Via a quadratic form construction, we characterize a one-parameter family of self-adjoint realizations of the corresponding Schroedinger operator, yielding admissible reduced Hamiltonians. We also discuss the implications for the related model describing a quantum particle immersed in a magnetic field with a local singularity of Aharonov-Bohm type. In this context, we provide a complete classification of all admissible Hamiltonians for a specific class of magnetic potentials.

Joint work with Michele Correggi (Politecnico di Milano).