# Observation of super-ballistic Brownian motion in liquid

## TL;DR

Researchers observed a new type of super-ballistic motion in liquids, where particles move faster than expected due to fluid memory effects.

## Contribution

The discovery of super-ballistic motion with t5/2 scaling due to fluid memory effects in nonequilibrium conditions.

## Key findings

- Super-ballistic motion with t5/2 scaling was theoretically predicted and experimentally confirmed.
- Colored noise in incompressible fluids leads to nonzero first moments for thermal forces.
- Nonequilibrium memory effects in fluids were revealed through mesoscopic particle motion.

## Abstract

Brownian motion is a foundational physical process characterized by a mean squared displacement that scales linearly in time in thermal equilibrium, known as diffusion. At short times, the mean squared displacement becomes ballistic, scaling as t2. This effect was predicted by Einstein in 1907 and recently observed experimentally. We report that this picture is only true on average; by conditioning specific initial velocities, we predict theoretically and confirm by experiment that the mean squared displacement becomes super-ballistic, with a power scaling law of t5/2. This result is due to the colored noise of incompressible fluids, resulting in a nonzero first moment for the thermal force when conditioned on nonzero initial velocities. These results are a step toward the unraveling of nonequilibrium dynamics of fluids.

The motion of mesoscopic particles in liquid reveals nonequilibrium memory effects in fluids.