From Short-Range to Contact Interactions in Many-Body Quantum Systems

Abstract: Many-body quantum systems with short-ranged two-body interactions, such as ultracold quantum gases are often described by simplified models with contact interactions (sometimes called delta-potentials). The merit of such models is their simplicity, solvability (to some extent) and lack of irrelevant or unknown detail. They are also toy models of renormalization. On the other hand, in dimensions $d\geq 2$ contact interactions are not small perturbations of the free energy, which makes their self adjoint implementation in the case of $N>2$ particles a subtle business. This talk gives an introduction to the mathematics of many-particle quantum systems with two-body contact interactions and their approximation by Schrödinger operators.

mathematical physics

Audience: researchers in the discipline

( video )

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