22. Sep 2026

On the three-body Hamiltonian for abelian anyons

Mathphys Analysis Seminar

Datum: 22. September 2026 | 16:15 – 17:15
Sprecher: Domenico Cafiero, Politecnico di Milano
Veranstaltungsort: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Sprache: Englisch

Anyons are 2d identical quantum particles with an intermediate exchange symmetry characterized by representations of the braid group. In the abelian case, they can be modelled through the so-called magnetic representation, namely as a system of bosons with an Aharonov-Bohm flux attached to each particle.
In this talk, I will discuss the construction of self-adjoint Hamiltonians, different from the Friedrichs realization, for a system of three abelian anyons. I will focus in particular on the Ter-Martirosyan-Skornyakov extensions. This family of Hamiltonians turns out to be parametrized by a suitable boundary operator; I will present a complete classification of its self-adjoint realizations and compute the negative spectrum for the specific case of interest. These results shed light on the possible occurrence of Thomas instability in the three-anyon model. Joint work with Michele Correggi (PoliMi) and Davide Fermi (PoliMi).