The Structure of Integrable One-Dimensional Systems

TL;DR

This paper explores the connection between classical integrable systems described by invariant tori and action-angle variables, and their quantum counterparts characterized by the asymptotic Bethe ansatz, highlighting their structural relationship.

Contribution

It clarifies the relationship between classical and quantum descriptions of integrable one-dimensional systems, bridging invariant tori and Bethe ansatz frameworks.

Findings

Classical invariant tori correspond to quantum Bethe ansatz solutions.

The paper establishes a structural link between classical and quantum integrability.

Insights into the spectral properties of integrable systems are provided.

Abstract

We explain the relationship between the classical description of an integrable system in terms of invariant tori and action-angle variables, and the quantum description in terms of the asymptotic Bethe ansatz.