Reservoir reduction of a polariton condensate

For reservoir kinetics ${\mathcal{R}}_t=-({\gamma }_R+R_{R}n)\mathcal{R}+P$, adiabatic elimination gives $\mathcal{R}=P/({\gamma }_R+R_{R}n)$. Expanding for $R_{R}n/{\gamma }_R\ll 1$ and inserting into the condensate equation gives a complex Ginzburg–Landau equation withFast reservoir response and weak depletion are separate assumptions. Without the number density expansion the gain is saturable, not cubic. The coefficients depend on position when the pump does.