Robert Seiringer, IST Austria

Quantum many-body systems with point interactions

We investigate the stability of quantum many-body systems with point interactions. In particular, we present a proof that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical value. For this impurity problem, we also show that the ground state energy of the system at given non-zero mean density differs from the one of the ideal gas by a term depending only on the density and the scattering length of the interactions, independently of N. While the general problem with more than one impurity remains open, we can show stability for the simplest such system, the one consisting of two fermions interacting with two (fermionic) impurities.

(Joint work with T. Moser)