# Quenches from gaussian bosons to Tonks-Girardeau gas: stationary states and effects of a confining potential

## TL;DR

This paper investigates the non-equilibrium dynamics of a Bose gas quenched from a Gaussian initial state to the Tonks-Girardeau regime, analyzing stationary states and effects of confinement using correlation functions and phase-space mapping.

## Contribution

It provides a comprehensive description of steady-state correlation functions after a quantum quench to the Tonks-Girardeau limit, including effects of a confining potential.

## Key findings

- Correlation functions expressed as Fredholm determinants
- Steady-state properties derived for quenched Bose gases
- Mapping of dynamics to classical phase-space in confinement

## Abstract

We consider the general problem of quenching an interacting Bose gas from the noninteracting regime to the strong repulsive case described by the Tonks-Girardeau limit, with the initial state being a gaussian ensemble for the bosons. A generic multi-point correlation function in the steady state can be fully described in terms of a Fredholm-like determinant suitable both for a numerical study and for an analytical study in certain limiting cases. Finally, we extend the study to the presence of a smooth confining potential showing that, in the thermodynamic limit, the time evolution of the two-point function can be mapped to a classical problem in a properly defined phase-space.