Jost solutions and quantum conserved quantities of an integrable derivative nonlinear Schrodinger model

TL;DR

This paper investigates quantum conserved quantities and Jost solutions in an integrable derivative nonlinear Schrödinger model, revealing a new coupling constant affecting quantum soliton properties and linking algebraic and coordinate Bethe ansatz results.

Contribution

It explicitly constructs quantum conserved quantities, introduces a novel coupling constant, and analyzes its impact on quantum soliton states in the DNLS model.

Findings

Quantum Hamiltonian features a new coupling constant.

Range of the coupling constant for positive soliton binding energy identified.

Established connections between algebraic and coordinate Bethe ansatz results.

Abstract

We study differential and integral relations for the quantum Jost solutions associated with an integrable derivative nonlinear Schrodinger (DNLS) model. By using commutation relations between such Jost solutions and the basic field operators of DNLS model, we explicitly construct first few quantum conserved quantities of this system including its Hamiltonian. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This modified coupling constant plays a crucial role in our comparison between the results of algebraic and coordinate Bethe ansatz for the case of DNLS model. We also find out the range of modified coupling constant for which the quantum $N$-soliton state of DNLS model has a positive binding energy.