Order by Disorder in Spin-Orbit Coupled Bose-Einstein Condensates

nding analytical expressions for the collective excitations in the long-wavelength limit and through numerical solution of the full Bogoliubov- de Gennes equations, we show that the system condenses into a single momentum state of the Rashba spectrum via the mechanism of order by disorder. We show that in 3D the quantum depletion for this system is small, while the thermal depletion has an infrared logarithmic divergence, which is removed for nite-size systems. In 2D, on the other hand, thermal uctuations destabilize the system.