The Mechanism of Complex Langevin Simulations
Abstract
We discuss conditions under which expectation values computed from a complex Langevin process Z will converge to integral averages over a given complex valued weight function. The difficulties in proving a general result are pointed out. For complex valued polynomial actions, it is shown that for a process converging to a strongly stationary process one gets the correct answer for averages of polynomials if cτ(k) E(eikZ(τ)) satisfies certain conditions. If these conditions are not satisfied, then the stochastic process is not necessarily described by a complex Fokker Planck equation. The result is illustrated with the exactly solvable complex frequency harmonic oscillator.
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