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 Schrödinger 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 latetime 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.

Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas / Del Vecchio Del Vecchio, G.; Bastianello, A.; De Luca, A.; Mussardo, G.. - In: SCIPOST PHYSICS. - ISSN 2542-4653. - 9:1(2020), pp. 1-37. [10.21468/SciPostPhys.9.1.002]

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

Del Vecchio Del Vecchio G.
;
Bastianello A.;De Luca A.;Mussardo G.
2020

Abstract

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 Schrödinger 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 latetime 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.
9
1
1
37
002
10.21468/SciPostPhys.9.1.002
https://arxiv.org/abs/2002.01423
Del Vecchio Del Vecchio, G.; Bastianello, A.; De Luca, A.; Mussardo, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128434
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