Proof of universality in one-dimensional few-body systems including anisotropic interactions

TL;DR

This paper analytically proves the universality of bound states in one-dimensional few-body systems with short-range interactions, demonstrating convergence to zero-range interaction results in the weak interaction limit.

Contribution

It provides the first analytical proof of universality for two- and three-particle systems in 1D with short-range interactions, including wave functions and energies.

Findings

Universality holds for weak short-range interactions in 1D systems.

Results converge to zero-range contact interaction solutions.

Proof covers both energies and wave functions.

Abstract

We provide an analytical proof of universality for bound states in one-dimensional systems of two and three particles, valid for short-range interactions with negative or vanishing integral over space. The proof is performed in the limit of weak pair-interactions and covers both binding energies and wave functions. Moreover, in this limit the results are formally shown to converge to the respective ones found in the case of the zero-range contact interaction.