Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas

• Main Author: Giuseppe Del Vecchio Del Vecchio, Alvise Bastianello, Andrea De Luca, Giuseppe Mussardo
• Format: Article
• Language: English
• Published: SciPost 2020-07-01
• Series: SciPost Physics
• Online Access: https://scipost.org/SciPostPhys.9.1.002

We study the out-of-equilibrium properties of a classical integrable non-relativistic theory, with a time evolution initially prepared with a finite energy density in the thermodynamic limit. The theory considered here is the Non-Linear Schrodinger equation which describes the dynamics of the one-dimensional interacting Bose gas in the regime of high occupation numbers. The main emphasis is on the determination of the late-time Generalised Gibbs Ensemble (GGE), which can be efficiently semi-numerically computed on arbitrary initial states, completely solving the famous quench problem in the classical regime. We take advantage of known results in the quantum model and the semiclassical limit to achieve new exact results for the momenta of the density operator on arbitrary GGEs, which we successfully compare with ab-initio numerical simulations. Furthermore, we determine the whole probability distribution of the density operator (full counting statistics), whose exact expression is still out of reach in the quantum model.