RESUMEN
In this reply, we respond to the comments by Lisý and Tóthová (LT) on our recent work [Phys. Rev. E 105, 064107 (2022)10.1103/PhysRevE.105.064107], where we have extended the microscopic theory of molecular motion in atomic liquids that was originally proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239]. Contrary to our conclusion of nonavailability of a physically tractable analytical solution of the equation of motion involving dynamic friction, LT have attempted to obtain an analytical solution giving the velocity autocorrelation function in liquids. We show that the analytical solution of the equation of motion derived by LT is incomplete and not an appropriate solution for the description of atomic dynamics in liquids. It is demonstrated that the generalized statements made by LT regarding the equation of motion giving incorrect results are unjustified in the absence of substantial proofs. Also, until and unless proven otherwise, we do not find any reason for the reconsideration of the theory as suggested by LT.
RESUMEN
A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.
