Wakefield of Bose-Einstein condensates in a background thermal gas

Wakefield excitation of sound waves by a Bose-Einstein (BE) condensate moving in a non-condensate gas is considered here. The BE condensate is described by a kinetic equation, which is valid in the quasi-classical limit. It describes the evolution of the Wigner function associated with its macroscopic wave-function. The non-condensate gas is described by fluid equations that are coupled to the kinetic equation by the mean field potential of the condensate. Wavefield solutions are established. Modulation instabilities occurring when the BE condensate beam velocity equals the sound velocity of the non-condensate gas are also considered. Cold and warm beam solutions for the instability growth rates are derived.