Related papers: Kernels and integration cycles in complex Langevin…
We analyze the pressure and density equations of state of unpolarized non-relativistic fermions at finite temperature in one spatial dimension. For attractively interacting regimes, we perform a third-order lattice perturbation theory…
In the field of machine learning coarse-grained potentials in molecular dynamics, many propagators require that the effective Hamiltonian is quadratic in momentum, thus limiting the family of coarse-graining functions. In this paper, we…
A lattice model is used to estimate the self-diffusivity of entangled cyclic and linear polymers in blends of varying compositions. To interpret simulation results, we suggest a minimal model based on the physical idea that constraints…
We study numerical methods for the generalized Langevin equation (GLE) with a positive Prony series memory kernel, in which case the GLE can be written in an extended variable Markovian formalism. We propose a new splitting method that is…
Stationary distributions of complex Langevin equations are shown to be the complexified path integral solutions of the Schwinger-Dyson equations of the associated quantum field theory. Specific examples in zero dimensions and on a lattice…
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…
Simulations of biophysical systems inevitably include steps that correspond to time integrations of ordinary differential equations. These equations are often related to enzyme action in the synthesis and destruction of molecular species,…
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
We discuss conditions under which expectation values computed from a complex Langevin process $Z$ will converge to integral averages over a given complex valued weight function. The difficulties in proving a general result are pointed out.…
The Complex Langevin (CL) method sometimes shows convergence to the wrong limit, even though the Schwinger-Dyson Equations (SDE) are fulfilled. We analyze this problem in a more general context for the case of one complex variable. We prove…
We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…
We present the results of continuum-extrapolated lattice simulations of quantum chromodynamics (QCD) above the crossover temperature and for unprecedentedly high baryon densities at the physical point, employing the complex Langevin…
In the framework of the problem of finding proper reaction coordinates (RCs) for complex systems and their effective evolution equations, we consider the case study of a polymer chain in an external double-well potential, experiencing…
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…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
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…
The complex Langevin method is one hopeful candidate to tackle the sign problem. This method is applicable not only to QCD but also to nonrelativistic field theory, such as condensed matter physics. We present the simulation results of a…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…