Exciton-polariton condensates are paradigmatic driven-dissipative systems. The complex Gross-Pitaevskii equation iℏ∂ψ/∂t = [−ℏ²∇²/2m + g|ψ|² + i(R−γ)/2]ψ balances gain R from the pump reservoir against loss γ. Above threshold, a steady-state condensate forms with spontaneous phase coherence despite constant particle turnover.
Complex GP equation:
iℏ∂ψ/∂t = [H₀ + g|ψ|² + i(R−γ)/2]ψ
Steady state condition:
R(n_R) = γ : gain = loss
n_ss = (P − P_th)/γ_R
Threshold: P_th = γ γ_R / R₀
Phase coherence:
KPZ universality class (1+1d)
Not true BEC — algebraic order