Low temperature kinetics of 2D exciton gas cooling in quantum well bilayer

We study the kinetics of 2D Bose gas cooling provided Bose particles interact with 3D phonons. At low temperatures phonon emission is prohibited by the energy and the momentum conservation. We show that both particle-particle scattering and impurity scattering assist Bose-gas cooling. The temporal relaxation of temperature follows the law $T\sim 1/\sqrt{t}$ above the Berezinski–Kosterlitz–Thouless phase transition point and $T\sim 1/t$ after a Bose-Einstein 2D quasi-condensate develops.