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

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.

arXiv commentDedicated to the memory of Prof. Renat M. Yulmetyev

References in corpus (4)

• A simple measure of memory for dynamical processes described by the generalized Langevin equation
• Fractional Calculus as a Macroscopic Manifestation of Randomness
• Steady-State Homogeneous Nucleation and Growth of Water Droplets: Extended Numerical Treatment
• Self-consistent approach to the description of relaxation processes in classical multiparticle systems