Effective Potential for Complex Langevin Equations

Understand

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.