Spectral problems for quantum particle systems with zero-range interactions

Alessandro Michelangeli (U Bonn)

Nov 10. 2022, 15:30 — 16:00

Ordinary multi-particle Schrödinger operators with two-body interaction potentials are studied in their spectral and dynamical features by means of sophisticated and yet today standard analytical and operator-theoretic tools that break down when the interaction is modelled to be only effective on a zero range and very large (infinite) scattering length -- a regime that has become fashionable and well achievable in contemporary cold-atom physics ("Unitary Gases"), and in turn triggered ad hoc heuristics, numerics, and mathematical analysis. General problems and a few case studies in this framework will be reviewed with emphasis on the needed mathematical apparatus (extension techniques, renomalisation-like limiting constructions, and other tools from modern operator theory).

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory of Differential Operators in Quantum Theory (Workshop)
Jussi Behrndt (TU Graz)
Fritz Gesztesy (Baylor U, Waco)
Ari Laptev (Imperial College London)
Christiane Tretter (U Bern)