Complex Langevin equations and Schwinger–Dyson equations

Complex Langevin Equations and Schwinger-Dyson Equations

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 are given. Relevance to the study of quantum field theory phase space is discussed.

Lattice Boltzmann-Langevin Equations

Intrinsic fluctuations around the solution of the lattice Boltzmann equation are described or modeled by addition of a white Gaussian noise source. For stationary states a fluctuation-dissipation theorem relates the variance of the fluctuations to the linearized Boltzmann collision operator and the pair correlation function.

Theory of KM2O-Langevin Equations, Complex Phenomena Described by Equations, and Stochastic Analysis of Mathematical Phenomena

Computing generalized Langevin equations and generalized Fokker-Planck equations.

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numeri...

Langevin Equations in Coarse-Graining

where z denotes the microscopic configuration and ρeq(z)dz is the equilibrium measure for the microscopic dynamics. In some cases the actual Hamiltonian (total energy) may be expressible in terms of the coarse-grained variables and is strictly conserved, but this is not always the case since some of the energy may in fact be incorporated in the coarse-grained free energy as an “entropy”. The eq...