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 in complex systems such as the motion of tracer
particles in living biological cells is nowadays measured with high
precision. Often the diffusion turns out to deviate from Einstein's laws.
This talk will discuss the basic mechanisms leading to such anomalous
diffusion as well as point out its consequences. In particular the
unconventional behaviour of non-ergodic, ageing systems will be discussed.
Indeed, non-ergodic diffusion in living cells has recently been demonstrated
experimentally.
