Generalized Langevin equation with hydrodynamic backflow: Equilibrium properties

The generalized Langevin equation with Gaussian fluctuations

It is shown that all statistical properties of the generalized Langevin equation with Gaussian fluctuations are determined by a single, two-point correlation function. The resulting description corresponds with a stationary, Gaussian, non-Markovian process. Fokker-Planck-like equations are discussed, and it is explained how they can lead one to the erroneous conclusion that the process is nonst...

Analytical solution of the generalized Langevin equation with hydrodynamic interactions: subdiffusion of heavy tracers.

We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynami...

Equilibration problem for the generalized Langevin equation

We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized classical Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is coupled to an infinite bath of harmonic oscillators which are initially in equilibrium. Using this equivalence we first determine the conditions neces...

Equilibrium properties of polymers from the Langevin equation: Gaussian self-consistent approach.

Langevin equation with Coulomb friction

We propose a Langevin model with Coulomb friction. Through the analysis of the corresponding Fokker-Planck equation, we have obtained the steady velocity distribution function under the influence of the external field.