Oscillations and negative velocity autocorrelation emerging from a Brownian particle model with hydrodynamic...

We study the dynamics of a particle in a fluid from a generalized Langevin equation (GLE) with a frictional exponential memory kernel and hydrodynamic interactions. By using Laplace analysis we obtain the analytical expressions for the velocity autocorrelation function (VACF) and mean square displacement (MSD) of the particle. Our results show that, in the strictly asymptotic time limit, the dynamics of the particle correspond to a particle ruled by a GLE with a Dirac delta friction memory kernel and hydrodynamic interactions. However, at intermediate times the dynamical behavior is qualitatively different due to the presence of a characteristic time in the frictional exponential memory kernel. Remarkably, the VACF exhibits oscillations and negative correlation regimes which are reminiscent of features already observed in pioneering works of molecular dynamics simulations. Moreover, ripples in the MSD appear as an emerging behavior associated with the mentioned regimes.