Higher conservation laws for the quantum non-linear Schroedinger equation

TL;DR

This paper discusses the higher conservation laws of the quantum non-linear Schrödinger equation, highlighting their historical discovery and recent applications in calculating three-body recombination rates in quantum gases.

Contribution

It revisits the known higher conservation laws of the quantum non-linear Schrödinger equation and emphasizes their relevance to current physical calculations.

Findings

Conservation laws are crucial for understanding quantum integrable systems.

These laws were known since 1989 and have recent applications in quantum gas research.

The paper provides historical context and references for these conservation laws.

Abstract

Quantum non-linear SCHROEDINGER equation is equivalent to Lieb-Liniger model. It has non-trivial conservation laws. Recently these conservation laws were used for evaluation of the three-body recombination rate for interacting gas of quantum bosons. These conservations laws were known already in 1989. Submitted text is retyping of the preprint of Centre for Mathematical Analysis of Australian National University CMA-R33-89. It was discussed in Leningrad Branch of the V.A. Steklov Mathematical Institute at that time. A copy of the original preprint can be found in the section Quantum Inverse Scattering Method of the web-page http://insti.physics.sunysb.edu/~korepin/