Quantum bound states for a derivative nonlinear Schrödinger model and number theory

Abstract

A derivative nonlinear Schrödinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant η. The ranges of η within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N≥3, the N-body bound states can have both positive and negative momenta. For η > 0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.