Exact Results for the Moments of the Rapidity Distribution in Galilean-Invariant Integrable Models

Abstract

We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit. Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a closed-form solution. We develop a general formalism enabling one to study the moments of the rapidity distribution, showing that they satisfy a difference-differential equation. The derived equation is explicitly analyzed in the case of the Lieb-Liniger model and the moments are analytically calculated. In addition, we obtained the exact information about the ground-state energy at weak repulsion. The obtained results directly enter a number of physically relevant quantities.

6 pages

References in corpus (3)

• Experimental Observation of a Generalized Gibbs Ensemble
• Generalized Gibbs Ensembles for Quantum Field Theories
• Method of difference-differential equations for some Bethe ansatz solvable models

Cited by in corpus (3)

• The full analytic trans-series in integrable field theories
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model