We derive, from first principle, the Fokker-Planck equation describing the non-perturbative real-time evolution of a gauge field at high temperatures on the spatial scale (g 2 T) −1 and the time scale (g 4 T) −1 , where g is the gauge coupling and T is the temperature. The knowledge of the effective dynamics on such spatial and time scales is crucial for the understanding and quantitative calcu...

A structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation is shown to go over to a Fokker-Planck equation for the description of Brownian motion at quantum level in the long wavelength limit. The structure of this ...

By using a rather simple algebraic approach, we revisit and further bridge between two most commonly used quantum dissipation theories, the Bloch–Redfield theory and a class of Fokker– Planck equations. The nature of the common approximation scheme involving in these two theories is analyzed in detail. While the Bloch–Redfield theory satisfies the detailed-balance relation, we also construct a ...

In this work we consider a nite element approach to solving the coupled Navier Stokes (NS) and Fokker Planck (FP) multiscale model that describes the dynamics of dilute polymeric uids. Deterministic approaches such as ours have not received much attention in the literature because they present a formidable computational challenge due to the fact that the analytical solution of the Fokker Planck...

The Fokker-Planck equation for the probability f(r,t) to find a random walker at position r at time t is derived for the case that the probability to make jumps depends nonlinearly on f(r,t) . The result is a generalized form of the classical Fokker-Planck equation where the effects of drift, due to a violation of detailed balance, and of external fields are also considered. It is shown that in...

We present a transport-based method for electrons that incorporates the correct transport mechanics and is computationally efficient for implementation in single event Monte Carlo codes. The method yields accurate dose profiles across a broad range of energies in heterogeneous media and presents a viable alternative to the established condensed history method. Our approach is mathematically rig...

The determination of the relaxation of electrons in atomic gases continues to be an important physical problem. The main interest is the determination of the time scale for the thermalization of electrons in different moderators and the nature of the time-dependent electron energy distribution. The theoretical basis for the study of electron thermalization is the determination of the electron d...

We introduce a class of generalized Fokker-Planck equations that conserve energy and mass and increase a generalized entropy functional until a maximum entropy state is reached. Nonlinear Fokker-Planck equations associated with Tsallis entropies are a special case of these equations. Applications of these results to stellar dynamics and vortex dynamics are proposed. Our prime result is a relaxa...

We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator as a problem of sparse linear algebra. Two variants are studied: a self-adjoint construction of the linear operator and the replacement of diffusion ...

We study the existence and the uniqueness of a solution φ to the linear Fokker-Planck equation −∆φ+ div(φF) = f in a bounded domain of R when F is a “confinement” vector field acting for instance like the inverse of the distance to the boundary. An illustration of the obtained results is given within the framework of fluid mechanics and polymer flows. Equation de Fokker-Planck dans un domaine b...