Dynamics of correlations in a dilute Bose gas following an interaction quench

We calculate the dynamics of the one and two body correlation functions in a homogeneous Bose gas at zero temperature following a sudden change in the interaction strength, with and without an underlying lattice. We focus on conceptually simple examples that highlight the features arising separately from interactions and band structure. In the continuum, we show that the Bogoliubov spectrum leads to a diffusive evolution of density correlations for short times, and ballistic at long times. In the lattice we find that the correlation functions develop additional oscillations. Moreover, the lattice dispersion induces an additional velocity scale, and some features instead propagate with that velocity. Finally, we discuss the time-evolution of the contact following a quench. Our predictions, which can be readily tested in experiments, serve as a benchmark for considering the dynamics of more complicated systems.