Nonequilibrium States of a Quenched Bose Gas*

Yin and Radzihovsky [Phys. Rev. A 88, 063611(2014)] recently developed a self-consistent extension of a Bogoliubov theory, in which the condensate number density, n$_{\mathrm{c}}$, is treated as a mean field that changes with time in order to analyze a JILA experiment by Makotyn et al. [Nature Physics doi:10.1038/nphys2850 (2014)] on a $^{85}$Rb Bose gas following a deep quench to a large scattering length. We apply this theory to construct a set of closed equations that highlight the role of dn$_{\mathrm{c}}$/dt, which is to induce an effective interaction between quasiparticles. We show analytically that such a system supports a steady state characterized by a constant condensate density and a steady but periodically changing momentum distribution, whose time average is described exactly by the generalized Gibbs ensemble. We discuss how the dn$_{\mathrm{c}}$/dt-induced effective interaction, which cannot be ignored on the grounds of the adiabatic approximation for modes near the gapless Goldstone mode, can affect experimentally measurable quantities such as Tan's contact.