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Effective potential for complex Langevin equations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2009Embargo end date: 01 Jan 2009 English Publisher:Elsevier BVJournal:Nuclear Physics B, volume 822, pages 349-366 (issn: 0550-3213, Copyright policy )
Authors: Guralnik, Gerald; Pehlevan, Cengiz;

doi: 10.1016/j.nuclphysb.2009.06.016 , 10.48550/arxiv.0902.1503

arXiv: 0902.1503

Effective potential for complex Langevin equations

Abstract

We construct an effective potential for the complex Langevin equation on a lattice. We show that the minimum of this effective potential gives the space-time and Langevin time average of the complex Langevin field. The loop expansion of the effective potential is matched with the derivative expansion of the associated Schwinger-Dyson equation to predict the stationary distribution to which the complex Langevin equation converges.

23 pages, 2 figures

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Keywords

High Energy Physics - Theory, Statistical Mechanics (cond-mat.stat-mech), High Energy Physics - Lattice (hep-lat), FOS: Physical sciences, Schwinger-dyson equations, Quantum field theory on lattices, Yang-Mills and other gauge theories in quantum field theory, High Energy Physics - Lattice, High Energy Physics - Theory (hep-th), Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, complex langevin equation, Condensed Matter - Statistical Mechanics

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 19
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    influence
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
19
Average
Top 10%
Top 10%
Green
gold