Effective potential for complex Langevin equations

We construct an effective potential for the complex Langevin equation on a lattice. We show that the minimum of this effective potential gives the space-time and Langevin time average of the complex Langevin field. The loop expansion of the effective potential is matched with the derivative expansion of the associated Schwinger-Dyson equation to predict the stationary distribution to which the complex Langevin equation converges. (C) 2009 Elsevier B.V. All rights reserved.