# A model solution of the generalized Langevin equation: Emergence and Breaking of Time-Scale Invariance in Single-Particle Dynamics of Liquids

## TL;DR

This paper derives a solution to the generalized Langevin equation that accounts for memory effects in single-particle dynamics of liquids, demonstrating its accuracy through molecular dynamics simulations of liquid tin and lithium.

## Contribution

It introduces a simple comparison-based method to solve the generalized Langevin equation, incorporating non-Markovity parameters to model memory effects in liquids.

## Key findings

- The derived velocity autocorrelation function matches molecular dynamics results.
- Memory effects significantly influence single-particle dynamics.
- The approach effectively captures time-scale invariance breaking.

## Abstract

It is shown that the solution of generalized Langevin equation can be obtained on the basis of simple comparison of the time scale for the velocity autocorrelation function of a particle (atom, molecule) and of the time scale for the corresponding memory function. The result expression for the velocity autocorrelation function contains dependence on the non-Markovity parameter, which allows one to take into account memory effects of the investigated phenomena. It is demonstrated for the cases of liquid tin and liquid lithium that the obtained expression for the velocity autocorrelation function is in a good agreement with the molecular dynamics simulation results.