On the instability of a homogeneous state of a weakly interacting Bose gas under external cooling

The behavior of a weakly interacting Bose gas with a finite particle lifetime has been studied in the framework of hydrodynamic equations under the conditions of a constant mass and energy inflow in the presence of external cooling. A spatially homogeneous state of such a gas is shown to be unstable with respect to the formation of an inhomogeneous density structure. A possible connection of the present results with experiments [3, 4] is discussed.