A powerful stochastic GP equation is under development to better understand many-body ground states and quench dynamics in spinor or spin-orbit coupled Bose-Einstein condensate.
As stochastic as it could or should be, we are puzzled for the Bosonic system at a finite temperature as how it finds its way 'home', stays put, and emerges with multiple vortices under spin-orbit couplings. To have some preliminary background, we recommend PB Blakie..... and CW Gardiner's review article for stochastic simulations of GP equations, where we hope to find the mechanism for vortices formation.