Currents of the Ablowitz-Ladik Chain

TL;DR

This paper derives explicit formulas for the densities of currents in the defocusing Ablowitz-Ladik chain and confirms the expected expressions for average currents in a generalized Gibbs ensemble.

Contribution

It provides the first explicit formulas for current densities and completes the proof for average current expressions in the Ablowitz-Ladik chain.

Findings

Explicit formulas for current densities derived.

Confirmed the expected average current expressions.

Enhanced understanding of integrable chain dynamics.

Abstract

While the currents of the defocusing Ablowitz-Ladik chain are unambiguously defined, no explicit formulas for their densities have been obtained yet. We close this gap. As a consequence, we also complete the argument which establishes the anticipated expression for average currents, averaged over a generalized Gibbs ensemble.