Ballistic Hot Brownian Motion

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Brownian motion is the erratic behavior of small particles suspended in a fluid caused by the numerous collisions with the surrounding molecules. Due to this cumulative effect of many individual uncorrelated events it is viewed as a prototype of a stochastic process in nature which meanwhile finds also application in financial market studies. The motion of a Brownian particle is fueled by thermal energy which is continuously exchanged between fluid and particle. Thus, the particles motion is also reflecting the temperature which is summarized by the Stokes Einstein relation connecting the diffusion coefficient with thermal energy and viscous friction. This relation holds for thermal equilibrium, where the temperature is constant in space. All degrees of freedom reflect the same temperature due to equipartition and even at very short timescales, when the motion of a particle is ballistic, the same temperature is found in the instantaneous velocity distribution. The situation is changed when the Brownian particle itself is a heat source or heat sink as it is the case for many chemically reacting species, plasmonic particles and active systems like microswimmers. The environment of the particle is no longer isothermal and it has been shown that the so called Hot Brownian Motion is governed by effective temperatures which are coupled to the hydrodynamics. Therefore, rotational and translational diffusion obey different effective temperatures and equipartition is no longer valid. This project aims at providing first experimental evidence for a frequency dependent effective temperature which allows for a generalized description of the motion of hot Brownian particles. In particular, we will study the transition to the ballistic regime of a heated Brownian particle. When entering this regime, the particle is influenced by the hydrodynamic flow it has generated itself. At even shorter timescales of ballistic motion the particle dynamics will be governed by the kinetic temperature in the instantaneous velocity distribution of Hot Brownian Motion. The relation of the effective temperature to the hydrodynamics suggests a frequency dependence of the effective temperature. Experimentally the particle dynamics shall be accessed by studying the fluctuations of a gold nanoparticle decorated polymer microparticle in an optical trap with nanosecond time and 15 picometer spatial resolution. The gold nanoparticles will be heated optically through their interaction with light. The results will provide for the first time a test of the theory of Hot Brownian Motion and give an experimental insight into a generalized description of non-isothermal Brownian motion by effective temperatures.