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Localised distributions and criteria for correctness in complex Langevin dynamics

Gert Aarts Orcid Logo, Pietro Giudice, Erhard Seiler

Annals of Physics, Volume: "337", Pages: 238 - 260

Swansea University Author: Gert Aarts Orcid Logo

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Abstract

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...

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Published in: Annals of Physics
ISSN: 00034916
Published: 2013
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa22578
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Abstract: 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.
Item Description: @articleAarts:2013uza, author = "Aarts, Gert and Giudice, Pietro and Seiler, Erhard", title = "Localised distributions and criteria for correctness in complex Langevin dynamics", journal = "Annals Phys.", volume = "337", pages = "238-260", doi = "10.1016/j.aop.2013.06.019", year = "2013", eprint = "1306.3075", archivePrefix = "arXiv", primaryClass = "hep-lat", SLACcitation = "%%CITATION = ARXIV:1306.3075;%%",
College: Faculty of Science and Engineering
Start Page: 238
End Page: 260