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

Abstract

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

39 pages, published in AHPO

References in corpus (5)

• Highly polarized Fermi gases in two dimensions
• The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions
• Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three
• A Many-body Problem with Point Interactions on Two Dimensional Manifolds
• On the Weakness of Short-Range Interactions in Fermi Gases

Cited by in corpus (5)

• Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three
• Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity
• On the Weakness of Short-Range Interactions in Fermi Gases
• Two dimensional delta Bose gas in a weighted space
• Hamiltonians for Quantum Systems with Contact Interactions