Unifying treatment of nonequilibrium and unstable dynamics of cold bosonic atom system with time-dependent order parameter in Thermo Field Dynamics

The coupled equations which describe the temporal evolution of the Bose–Einstein condensed system are derived in the framework of nonequilibrium Thermo Field Dynamics. The key element is that they are not the naive assemblages of assumed equations, but are the self-consistent ones derived by appropriate renormalization conditions. While the order parameter is time-dependent, an explicit quasiparticle picture is constructed by a time-dependent expansion. Our formulation is valid even for the system with a unstable condensate, and describes the condensate decay caused by the Landau instability as well as by the dynamical one.

Research highlights
► Cold atoms with time-dependent condensate in nonequilibrium Thermo Field Dynamics.
► Coupled equations which describe the temporal evolution of the system are derived.
► They are not the naive assemblages of presumable equations, but the self-consistently ones.
► Valid even for systems with Landau or dynamical instability, and describing decays.
► Transport equation has new collision term that is important in Landau instability.