Short-time dynamics of a tracer in an ideal gas

A small tagged particle immersed in a fluid exhibits Brownian motion and diffuses on a long timescale. Meanwhile, on a short timescale, the dynamics of the tagged particle cannot be simply described by the usual generalized Langevin equation with Gaussian noise, since the number of collisions between the tagged particle and fluid particles is rather small. On such a timescale, we should explicitly consider individual collision events between the tagged particle and the surrounding fluid particles. In this study we analyze the short-time dynamics of a tagged particle in an ideal gas, where we do not have static or hydrodynamic correlations between fluid particles. We perform event-driven hard-sphere simulations and show that the short-time dynamics of the tagged particle is correlated even under such an idealized situation. Namely, the velocity autocorrelation function becomes negative when the tagged particle is relatively light and the fluid density is relatively high. This result can be attributed to the dynamical correlation between collision events. To investigate the physical mechanism which causes the dynamical correlation, we analyze the correlation between successive collision events. We find that the tagged particle can collide with the same ideal-gas particle several times and such collisions cause a strong dynamical correlation for the velocity.