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，它被视为自然界随机过程的原型，同时也在金融市场研究中得到应用。布朗粒子的运动是由不断在流体和粒子之间交换的热能推动的。因此，粒子的运动也反映了温度，这可以用斯托克斯-爱因斯坦关系来概括，它将扩散系数与热能和粘性摩擦联系起来。这种关系适用于热平衡，即温度在空间中保持恒定。由于均分，所有的自由度都反映相同的温度，即使在很短的时间尺度上，当粒子的运动是弹道运动时，在瞬时速度分布中也发现相同的温度。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质、等离子体粒子和活性系统（如微游泳体）都是如此。粒子的环境不再是等温的，并且已经表明，所谓的热布朗运动是由与流体力学耦合的有效温度控制的。因此，旋转和平动扩散服从不同的有效温度，均分不再有效。该项目旨在为频率相关的有效温度提供第一个实验证据，该有效温度允许对热布朗粒子的运动进行广义描述。特别地，我们将研究热布朗粒子向弹道态的跃迁。当进入这一状态时，粒子受到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，粒子动力学将受热布朗运动瞬时速度分布中的动力学温度的支配。有效温度与流体力学的关系表明，有效温度具有频率依赖性。通过实验研究金纳米粒子修饰的聚合物微粒在纳秒时间和15皮米空间分辨率的光阱中的波动，可以获得粒子动力学。金纳米颗粒将通过与光的相互作用而被光学加热。该结果将首次对热布朗运动理论进行检验，并通过有效温度对非等温布朗运动的广义描述提供实验见解。

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 Therefore, rotational and translational diffusion obey different effective temperatures and equipartition is no longer valid.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