Quenches from bosonic Gaussian initial states to the Tonks-Girardeau limit: Stationary states and effects of a confining potential

We consider the general problem of quenching an interacting Bose gas from the noninteracting regime to the strongly repulsive limit described by the Tonks-Girardeau gas with the initial state being a Gaussian ensemble in terms of the bosons. A generic multipoint correlation function in the steady state can be described fully in terms of a Fredholm-like determinant suitable both for a numerical 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.