Localised distributions and criteria for correctness in complex Langevin dynamics

Journal Article · Tue Oct 15 04:00:00 EDT 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.06.019· OSTI ID:22224222

Aarts, Gert ^[1]; Giudice, Pietro ^[1]; Seiler, Erhard ^[2]

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1. Department of Physics, College of Science, Swansea University, Swansea (United Kingdom)
2. Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany)

Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker–Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected. -- Highlights: •Characterisation of the equilibrium distribution sampled in complex Langevin dynamics. •Connection between criteria for correctness and breakdown. •Solution of the Fokker–Planck equation in the case of real noise. •Analytical determination of support in complexified space.

• OSTI ID: 22224222
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 337; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
COMPUTERIZED SIMULATION
EQUILIBRIUM
FOKKER-PLANCK EQUATION
NOISE
SPACE
STOCHASTIC PROCESSES