Cole Thumann Qualifying Exam

Abstract: At short timescales, the overdamped description of Brownian motion breaks down, revealing the ballistic transport of the particle. Furthermore, when the density of the Brownian particle is comparable to the surrounding Newtonian liquid, fluid inertia couples with the particle's dynamics, giving rise to an effective added mass, a history-dependent Basset-Boussinesq force, and colored thermal noise. In this talk, we present direct experimental observations of these non-Markovian hydrodynamic effects using a barium titanate microsphere optically trapped in acetone. By employing a high-bandwidth split-beam detection scheme, we resolve the particle's velocity well below its momentum relaxation time. We analyze the fractal nature of the equilibrium velocity time series, finding a characteristic t^(-3/4) power law scaling in length resolution. Next, by preferentially conditioning sub-ensembles of trajectories on near-zero initial velocities, we temporarily suppress deterministic dissipation, revealing a super-ballistic mean squared displacement that scales as t^(5/2).  Finally, we will discuss ongoing experimental efforts to trap silver coated microspheres for nonequilibrium tests at even shorter timescales.