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In recent years, there has been remarkable progress in theoretical justification of the complex Langevin method, which is a promising method for evading the sign problem in the path integral with a complex weight. There still remains, however, an issue concerning occasional failure of this method in the case where the action involves logarithmic singularities such as the one appearing from the fermion determinant in finite density QCD. In this talk, we point out that this failure is due to the breakdown of the relation between the complex weight which satisfies the Fokker-Planck equation and the probability distribution generated by the stochastic process. In fact, this kind of failure can occur in general when the stochastic process involves a singular drift term. We show, however, in simple examples, that there exists a parameter region in which the method works although the standard reweighting method is hardly applicable.
The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the presence of loga
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooli
Recently there has been remarkable progress in solving the sign problem, which occurs in investigating statistical systems with a complex weight. The two promising methods, the complex Langevin method and the Lefschetz thimble method, share the idea
The complex Langevin method and the generalized Lefschetz-thimble method are two closely related approaches to the sign problem, which are both based on complexification of the original dynamical variables. The former can be viewed as a generalizatio
The complex Langevin method (CLM) provides a promising way to perform the path integral with a complex action using a stochastic equation for complexified dynamical variables. It is known, however, that the method gives wrong results in some cases, w