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

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