Multi-band structure of the quantum bound states for a generalized nonlinear Schrodinger model

TL;DR

This paper investigates the structure of N-body bound states in a generalized nonlinear Schrödinger model, revealing their existence across various parameter ranges and employing number theory for analysis.

Contribution

It introduces a novel analysis of bound state bands in a nonlinear Schrödinger model using Farey sequences, expanding understanding of their parameter dependence.

Findings

Bound states exist for all c and specific η ranges.

Bound states can have positive or negative momentum and energy.

Farey sequences determine the η ranges for bound states.

Abstract

By using the method of coordinate Bethe ansatz, we study N-body bound states of a generalized nonlinear Schrodinger model having two real coupling constants c and \eta. It is found that such bound states exist for all possible values of c and within several nonoverlapping ranges (called bands) of \eta. The ranges of \eta within each band can be determined completely using Farey sequences in number theory. We observe that N-body bound states appearing within each band can have both positive and negative values of the momentum and binding energy.