Related papers: Correctness criteria for complex Langevin
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
The complex Langevin method is a general method to treat systems with complex action, such as QCD at nonzero density. The formal justification relies on the absence of certain boundary terms, both at infinity and at the unavoidable poles of…
We investigate the applicability of complex Langevin dynamics to the three-dimensional XY model at finite chemical potential. To assess correctness, we introduce a new diagnostic based on the configurational temperature (or configurational…
Complex Langevin simulations provide an alternative to sample path integrals with complex weights and therefore are suited to determine the phase diagram of QCD from first principles. We use our proposed method of Dynamic Stabilisation (DS)…
Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…
We show that complex Langevin simulation converges to a wrong result, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of…
The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown…
The complex Langevin (CL) method shows significant potential in addressing the numerical sign problem. Nonetheless, it often produces incorrect results when used without any stabilization techniques. Leveraging insights from previous…
Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromo-dynamics at finite density to the non-equilibrium evolution of quantum systems.…
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…
We present our latest results on the application of the complex Langevin method to one- and two-dimensional QCD. Although the method is stable, it unfortunately converges to an incorrect result when applied as such. After applying…
The ability to describe strongly interacting matter at finite temperature and baryon density provides the means to determine, for instance, the equation of state of QCD at non-zero baryon chemical potential. From a theoretical point of…
A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…
Progress in the application of the complex Langevin method to full QCD at non-zero chemical potential is reported. The method evades the sign problem which makes naive simulations at nonzero density impossible. The procedure 'gauge cooling'…
We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…
The sign problem of QCD prevents standard lattice simulations to determine the phase diagram of strong interactions with a finite chemical potential directly. Complex Langevin simulations provide an alternative method to sample path…
The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring…
From microscopic models, a Langevin equation can in general be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier…