From Short-Range to Contact Interactions in the 1d Bose Gas

Abstract

For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schrödinger operators with rescaled two-body potentials, and we estimate the rate of this convergence.

arXiv comment23 pages

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Cited by in corpus (8)

• Models of zero-range interaction for the bosonic trimer at unitarity
• Three-Body Hamiltonian with Regularized Zero-Range Interactions in Dimension Three
• From Short-Range to Contact Interactions in Two-dimensional Many-Body Quantum Systems
• Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity
• On the effect of repulsive interactions on Bose-Einstein condensation in the Luttinger-Sy model
• 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