Ballistic Hot Brownian Motion

布朗运动是悬浮在流体中的小颗粒由于与周围分子的多次碰撞而产生的不稳定行为。由于许多独立的不相关事件的累积效应，它在自然界中被视为随机过程的原型，同时在金融市场研究中也有应用。布朗粒子的运动是由热能推动的，热能在流体和粒子之间不断交换。因此，粒子的运动也反映了温度，而温度是由将扩散系数与热能和粘性摩擦联系起来的斯托克斯·爱因斯坦关系来总结的。这个关系适用于热平衡，即空间中的温度是恒定的。由于均分，所有的自由度都反映了相同的温度，即使在很短的时间尺度上，当粒子的运动是弹道的时，在瞬时速度分布中也可以发现相同的温度。当布朗粒子本身是热源或热沉时，情况就改变了，因为许多化学反应物种、等离子粒子和活动系统，如微泳者，都是这种情况。粒子的环境不再是等温的，已经证明所谓的热布朗运动是由与流体力学耦合的有效温度所支配的。因此，旋转扩散和平移扩散服从不同的有效温度，均分不再有效。这个项目的目的是为频率相关的有效温度提供第一个实验证据，它允许对热布朗粒子的运动进行普遍的描述。特别是，我们将研究受热布朗粒子向弹道区域的转变。当进入这一区域时，颗粒受到其自身产生的流体动力流的影响。在更短的弹道运动时间尺度上，粒子动力学将由热布朗运动瞬时速度分布中的动力学温度所支配。有效温度与流体动力学的关系表明，有效温度与频率有关。在实验上，通过研究纳米金修饰聚合物微粒在时间为纳秒、空间分辨率为15皮米的光学陷阱中的涨落来获得粒子动力学。金纳米粒子将通过与光的相互作用被光学加热。这些结果将首次验证热布朗运动理论，并为有效温度对非等温布朗运动的广义描述提供实验依据。

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 Therefore, rotational and translational diffusion obey different effective temperatures and equipartition is no longer valid.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.