Nonlinear Phenomena in Complex Systems, 2016, Vol.19, No.3, pp.278-285

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2016, Vol.19, No.3, pp.278-285

A Model Solution of the Generalized Langevin Equation: Emergence and Breaking of Time-Scale Invariance in Single Particle Dynamics of Liquids
A. V. Mokshin and B. N. Galimzyanov

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.

Key words: memory effects, stochastic processes, non-linear dynamics, non-Markovian processes, velocity autocorrelation function, molecular dynamics

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