Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel

Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel.

Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrator...

Stochastic Quantization of Topological Field Theory: Generalized Langevin Equation with Memory Kernel

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. PACS numbers: 03.70+k, 04.62.+v e-mail: [email protected] e-mail: [email protected]

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...

A Numerical Integration Method by Using Generalized Series of Functions

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...