Complex Langevin and boundary terms

• Verfasst von: Scherzer, Manuel [VerfasserIn]
• Verfasst von: Stamatescu, Ion-Olimpiu [VerfasserIn]
• Titel: Complex Langevin and boundary terms
• Verf.angabe: Manuel Scherzer, Erhard Seiler, Dénes Sexty, and Ion-Olimpiu Stamatescu
• E-Jahr: 2019
• Jahr: 24 January 2019
• Umfang: 12 S.
• Fussnoten: Gesehen am 11.09.2020
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Woodbury, NY : Inst., 2016
• Jahr Quelle: 2019
• Band/Heft Quelle: 99(2019,1) Artikel-Nummer 014512, 12 Seiten
• ISSN Quelle: 2470-0029
• DOI: doi:10.1103/PhysRevD.99.014512
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 158769266X

Abstract

As is well known the complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, we analyze the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. We also show how some simple modification stabilizes the CL process in such a way that it can produce results agreeing with direct integration. Besides explicitly demonstrating the connection between boundary terms and correct convergence our analysis also suggests a correctness criterion which could be applied in realistic lattice simulations.