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.
Cited by 5
Bastianello et al., Thermalization of a Trapped One-Dimensional Bose Gas via Diffusion
Phys. Rev. Lett. 125, 240604 (2020) [Crossref]
Koch et al., Adiabatic formation of bound states in the one-dimensional Bose gas
Phys. Rev. B 103, 165121 (2021) [Crossref]
Baldovin et al., Statistical Mechanics of an Integrable System
J Stat Phys 183, 41 (2021) [Crossref]
Konik et al., Approaching the self-dual point of the sinh-Gordon model
J. High Energ. Phys. 2021, 14 (2021) [Crossref]
Bastianello et al., Generalized hydrodynamics with dephasing noise
Phys. Rev. B 102, 161110 (2020) [Crossref]
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- 1 King's College London [KCL]
- 2 Institute of Physics, University of Amsterdam [IoP, UvA]
- 3 CY Cergy Paris Université / CY Cergy Paris University
- 4 Istituto Nazionale di Fisica Nucleare (presso la SISSA) / National Institute of Nuclear Physics (at SISSA) [INFN at SISSA]