MPIDS Seminar: Don’t average! --- Learning from fluctuations in diffusive processes

After a brief introduction to the history of Brownian motion I will address current challenges to the physical understanding of diffusive processes in complex systems. These challenges arise from mod-ern experimental techniques such as single particle tracking as well as supercomputing studies. Typi-cally, these approaches provide relatively few trajectories of tracer particles, of finite measurement time. Evaluating individual trajectories, for instance, in terms of time-averaged mean squared dis-placements, the results will naturally fluctuate from one trajectory to another. Instead of averaging further over all measured trajectories, I will argue that one can extract valuable information from these fluctuations, helping us to decipher the physical mechanisms behind the observed particle mo-tion, including measurement noise. For both normal and anomalous diffusion the exact form of these fluctuations will be discussed for measured moments as well as the single-trajectory power spectrum. Moreover, the emergence of non-Gaussian forms of the displacement distribution due to inhomogeneous environments will be addressed. In a similar spirit I will argue that cognisance of the entire distribution of reaction times is vital for the understanding of low-concentration chemical re-actions, rather than focusing on mean reaction rates. Finally, current data science approaches to the analysis of diffusing data are introduced in terms of Bayesian and machine learning techniques.