1992/11/18 by H. Gausterer, Sean Lee · 20 citations
Mathematics · Physics and Astronomy · #Complex system #Harmonic #Langevin dynamics #Markov Chains and Monte Carlo Methods #Mechanism (biology) #Polynomial #Process (computing) #Statistical Mechanics and Entropy #Stochastic process #hep-lat #stochastic dynamics and bifurcation
paper · pdf · doi:10.1007/bf01052754
published in Journal of Statistical Physics 73(1-2), 147-157 (Springer Science+Business Media) · 12 p, UNIGRAZ-UTP-290992
arxiv created 1992/11/18 · openalex publication_date 1993/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.