abstract: In 1905 Einstein formulated the laws of diffusion, and in 1908 Perrin published his Nobel-prize winning studies determining Avogadro's number from diffusion measurements. With similar, more refined techniques the diffusion behaviour of submicron tracer particles or even single molecules is now routinely measured in the complex environment of living biological cells and similarly complex systems. It is frequently observed that the passive diffusion of such particles deviates from Einstein's laws.
This talk will discuss the basic mechanisms leading to such anomalous diffusion as well as point out its physical consequences. In particular, it will be discussed how we can understand the experimental observation of weakly non-ergodic behaviour (time and ensemble averages of physical observables behave differently) and ageing (physical observables depend on the time span between initial preparation of the system and start of the measurement).