Theoretical concepts to deal with stochastic, correlation and memory effects in nanoscale- and bio-physics systems (liquids, proteins, organisms) will be introduced and discussed. These concepts will be applied to experiments that probe the motion of particles or organisms, the structure and spectroscopic properties of liquids and chemical or conformational transitions. Concepts will be explained in the lectures, detailed theoretical derivations will be presented in handouts that will be discussed in the tutorial. Analytical theory will be compared with numerical approaches and simulations. The exam will take place in terms of a homework that can be chosen from the different topics covered in class.
- Brownian motion in liquids and complex systems
classical Brownian theory
stochastic theory for financial and meteorological time series data
motion of living organisms
environmental memory effects, aging
normal and anomalous diffusion
- Central limit theorem, equipartition theorem, deviations from Gaussian distributions on the nanoscale
- Correlations in interacting liquids
Ornstein-Zernike theory, classical density functional theory, scattering functions
- Rare events, non-linear effects
barrier crossing events
chemical reaction kinetics in liquids
protein folding
- Spectroscopy
harmonic damped oscillator
anharmonic effects
homogeneous versus inhomogeneous line broadening
spectral life times
- Non-equilibrium systems
approach to equilibrium
stationary non-equilibrium systems