  Stochastic quantization can potentially be used to simulate theories with a
complex action due to a nonzero chemical potential. We study complex Langevin
dynamics in the relativistic Bose gas analytically, using a mean field
approximation. We concentrate on the region with a Silver Blaze problem and
discuss convergence, stability, fixed points, and the severeness of the sign
problem. The real distribution satisfying the extended Fokker-Planck equation
is constructed and its nonlocal form is explained. Finally, we compare the mean
field results in finite volume with the numerical data presented in Ref. [1].
