Reply to "Comment on 'Brownian motion with time-dependent friction and single-particle dynamics in liquids' ".

In this reply, we respond to the comments by Lisý and Tóthová (LT) on our recent work [Phys. Rev. E 105, 064107 (2022)10.

Brownian motion with time-dependent friction and single-particle dynamics in liquids.

A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.

Velocity autocorrelation function for simple liquids and its application to liquid metals and alloys.

The single-particle Brownian motion in simple monatomic liquids has been described with the help of the equation of motion in terms of velocity autocorrelation function psi(t) , where the particle is assumed to diffuse in a mean-time-dependent field. The equation of motion which is a second order differential equation in psi(t) has been solved in terms of nth order Bessel functions of the first and second kind. The solution is, in fact, the generalization of the solution given by Glass and Rice (GR) [Phys.