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Article Dans Une Revue Physical Review Letters Année : 2023

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

Résumé

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.

Dates et versions

hal-03940333 , version 1 (16-01-2023)

Identifiants

Citer

Zoran Ristivojevic. Exact Results for the Moments of the Rapidity Distribution in Galilean-Invariant Integrable Models. Physical Review Letters, 2023, 130 (2), pp.020401. ⟨10.1103/PhysRevLett.130.020401⟩. ⟨hal-03940333⟩
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