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

TL;DR

This paper demonstrates that a derivative nonlinear Schrödinger model supports localized N-body bound states within specific coupling constant ranges, which are characterized using number theory, revealing new insights into their momentum and energy properties.

Contribution

It introduces a novel connection between the existence of bound states in a nonlinear Schrödinger model and number theoretic concepts like Farey sequences and continued fractions.

Findings

Bound states exist within specific eta ranges determined by number theory.

States can have both positive and negative momentum for N > 2.

Positive momentum states have positive binding energy, negative momentum states have negative binding energy.

Abstract

A derivative nonlinear Schrodinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant eta. The ranges of eta within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N > 2, the N-body bound states can have both positive and negative momentum. For eta > 0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.