Brownian dynamics with memory

The classical theory of Brownian motion is based on the Markovian hypothesis of the underlying stochastic process, implying short time memory effects. Diffusion processes in complex systems, such as biological macromolecules, are, in contrast, characterised by long-time memory effects which lead to an algebraic decay of the respective correlation functions. Recent simulation results show the meaning of "complexity" in this context and demonstrate that fractional Brownian dynamics is a good model for the internal dynamics of proteins. The model can be applied on the short pico- to nanosecond time scale seen by quasielastic neutron scattering, as well as on the millisecond to second time scale seen by single molecule fluorescence spectroscopy. The results are discussed from astatistical physics point of view and possibilities for applications to the analysis of macroscopic transport processes are outlined.