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

TL;DR

This paper demonstrates that two-dimensional many-body quantum systems with contact interactions can be derived as limits of Schrödinger operators with scaled pair potentials, providing a rigorous mathematical foundation for these models.

Contribution

It establishes a rigorous limit process connecting Schrödinger operators with scaled potentials to contact interaction models in two dimensions.

Findings

Contact interactions arise as norm resolvent limits of scaled Schrödinger operators.

The results provide a mathematical foundation for contact interaction models in 2D quantum systems.

The approach applies to systems with multiple particles and specific potential rescaling.

Abstract

Quantum systems composed of $N$ distinct particles in $\R^2$ with two-body contact interactions of TMS type are shown to arise as limits - in the norm resolvent sense - of Schr\"odinger operators with suitably rescaled pair potentials.