A simple measure of memory for dynamical processes described by the generalized Langevin equation

TL;DR

This paper introduces a straightforward measure to quantify memory effects in dynamical systems described by the generalized Langevin equation, with applications to physical models exhibiting long-time correlations and anomalous diffusion.

Contribution

A new simple measure for estimating memory effects in systems governed by the generalized Langevin equation is proposed and numerically validated.

Findings

The measure effectively captures memory effects in various physical models.

It provides insights into long time tail phenomena and anomalous diffusion.

Numerical results demonstrate the measure's applicability and accuracy.

Abstract

Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory effects is introduced within the framework of this description. Numerical calculations of the suggested measure and the analysis of memory effects are also applied for various model physical systems as well as for the phenomena of ``long time tails'' and anomalous diffusion.