Quantum fluctuations of the out-of-equilibrium one-dimensional Bose gas described by Generalized Hydrodynamics

Abstract

^*Considerable progress has taken place recently in modeling the large-scale dynamics of one-dimensional quantum many-body systems that are integrable or nearly integrable, thanks to the advent of Generalized Hydrodynamics. In particular, Generalized Hydrodynamics provides a computationally efficient tool for simulating experiments on one-dimensional Bose gases. Like any other hydrodynamic theory, it consists of a simplified description of the gas in terms of a reduced number of thermodynamic quantities that depend continuously on position, and evolve according to classical Euler equations. Here we aim at reconstructing some of the features of the quantum fluid that are lost in that description, in particular the quantum fluctuations and correlations at equal time that originate from the propagation of phonons in the fluid. The resulting framework takes the form of a spatially- and time-dependent multi-component Luttinger liquid, which can be used to efficiently compute correlation funct