2016/06/30 by Keitaro Nagata, Jun Nishimura, Shinji Shimasaki · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Applied mathematics #Argument (complex analysis) #Calculus (dental) #Chemistry #Computer science #Convergence (economics) #Econometrics #Economics #Mathematical Analysis and Transform Methods #Mathematical economics #Mathematics #Physics #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #Statistical physics #hep-lat
paper · pdf · doi:10.1103/physrevd.94.114515
published as Phys. Rev. D 94, 114515 (2016) · 34 pages, 8 figures. The version accepted for publication in PRD
arxiv created 2016/12/11 · openalex publication_date 2016/12/27 · arxiv updated 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted range of applicability, the use of gauge cooling made it applicable to various interesting cases including finite density QCD in certain parameter regions. In this paper we revisit the argument for justification of the method. In particular, we point out a subtlety in the use of time-evolved observables, which play a crucial role in the previous argument. This requires that the probability of the drift term should fall off exponentially or faster at large magnitude. We argue that this is actually a necessary and sufficient condition for the method to be justified. Using two simple examples, we show that our condition tells us clearly whether the results obtained by the method are trustable or not. We also discuss a new possibility for the gauge cooling, which can reduce the magnitude of the drift term directly.