Clusters of bound particles in the derivative delta-function Bose gas

TL;DR

This paper introduces a new method to construct particle clusters in a one-dimensional derivative delta-function Bose gas, linking special coupling constants to Farey sequences, and analyzes their properties and stability.

Contribution

It presents a novel procedure for forming bound particle clusters at specific coupling constants using equidistant quasi-momenta on a circle, connecting physics with number theory.

Findings

Clusters form at special coupling constants related to Farey sequences.

The size and stability of clusters depend on the coupling constant.

A classification scheme for clusters based on number theory is developed.

Abstract

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative delta-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative delta-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant.