Related papers: Complex Langevin dynamics: criteria for correctnes…
We study full QCD at finite density and low temperature with light quark mass using the complex Langevin method. Since the singular drift problem turns out to be mild on a $4^3 \times 8$ lattice we use, the gauge cooling is performed only…
Rotating systems in thermal equilibrium are ubiquitous in our world. In the context of high energy physics, rotations would affect the phase structure of QCD. However, the standard Monte-Carlo methods in rotating systems are problematic…
Our knowledge about the QCD phase diagram at finite baryon chemical potential $\mu_{B}$ is limited by the well known sign problem. The path integral measure, in the standard determinantal approach, becomes complex at finite $\mu_{B}$ so…
Systems governed by a multivariate Langevin equation featuring an exact potential exhibit straightforward dynamics but are often difficult to recognize because, after a general coordinate change, the gradient flow becomes obscured by the…
The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass. In order to understand its property, we consider the sign problem of the one-site fermion…
We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method…
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…
We study the exponential convergence to the stationary state for nonequilibrium Langevin dynamics, by a perturbative approach based on hypocoercive techniques developed for equilibrium Langevin dynamics. The Hamiltonian and overdamped…
In this thesis, we study the critical dynamics near the QCD critical point. Near the critical point, the relevant modes for the critical dynamics are identified as the hydrodynamic modes. Thus, we first study the linear dynamics of them by…
We investigate methods for variance reduction and the elimination of systematic error in a Fourier accelerated Langevin scheme for general spin models. We present results for the $SU(3)\times SU(3)/SU(3)$ model in two-dimensions that are…
To leading order in perturbation theory, we solve QCD, defined on a small three sphere in the large N and Nf limit, at finite chemical potential and map out the phase diagram in the (mu,T) plane. The action of QCD is complex in the presence…
In the numerical simulation of certain field theoretical models, the complex Langevin simulation has been believed to fail due to the violation of ergodicity. We give a detailed analysis of this problem based on a toy model with one degree…
Recently, cluster methods have been used to solve a variety of sign problems including those that arise in the presence of fermions. In all cases an analytic partial re-summation over a class of configurations in the path integral was…
The sign problem is notorious in Monte Carlo simulations of lattice QCD with the finite density, lattice field theory (LFT) with a $\theta$ term and quantum spin models. In this report, to deal with the sign problem, we apply the maximum…
Standard lattice fermion algorithms run into the well-known sign problem at real chemical potential. In this paper we investigate the possibility of using imaginary chemical potential, and argue that it has advantages over other methods,…
Lattice models with complex actions are important for the understanding of matter at finite densities, but not accessible by the standard Monte Carlo techniques due to the sign problem. Here we derive a new approach for avoiding the complex…
We prove, under mild conditions, that the stochastic gradient Langevin dynamics converges to a limiting law as time tends to infinity, even in the case where the driving data sequence is dependent.
Lattice QCD at finite baryon chemical potential has the infamous sign problem which hinders Monte Carlo simulations. This can be remedied by a dual representation that makes the sign problem mild. In the strong coupling limit, the dual…
Lattice QCD at finite density suffers from a severe sign problem, which has so far prohibited simulations of the cold and dense regime. Here we study the onset of nuclear matter employing a three-dimensional effective theory derived by…
In many interesting physical systems, the determinant which appears from integrating out fermions becomes complex, and its phase plays a crucial role in the determination of the vacuum. An example of this is QCD at low temperature and high…