Stochastic dynamics

winter term 2021/2022
Lecturer: Schwarz
Link to LSF
34 participants

Stochastic dynamics is the study of dynamical processes that occur on sufficiently large time scales such that the fast microscopic degrees of freedom can effectively be described as stochastic noise. The paradigmatic case is the diffusion of a Brownian particle in a fluid. Two fundamentally different yet equivalent differential equations describe this situation: the Fokker-Planck equation (a partial differential equation, PDE) and the Langevin equation (a stochastic differential equation, SDE, that requires stochastic calculus). For processes with jumps, one deals with a master equation. This lecture offers an introduction into all three types of equations. We also will cover many applications, including examples from biophysics and econophysics. A background in statistical physics is helpful but not required to attend this lecture.

Script and introduction

A script is available from earlier versions of this course. The covered material will be similar, but there are always changes and new subjects, plus we are happy for suggestions what else to include.

We also upload the PDF-file of the introduction from Oct 18 2021, in which we explain the motivation and content of this course, the technical details and the relevant literature.

Book recommendations

Here is a list of helpful text books. The first one is our favorite, but out of print:
  • J. Honerkamp, Stochastische Dynamische Systeme, VCH 1990
  • W. Paul and J. Baschnagel, Stochastic Processes: From Physics to Finance, Springer 1999
  • R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford University Press 2001
  • C.W. Gardiner, Handbook of stochastic methods, Springer 2004
  • N.G. van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier 1992
  • W. Horsthemke und R. Lefever, Noise-induced transitions. Theory and Applications in Physics, Chemistry, and Biology, Springer 1984
  • H. Risken, The Fokker-Planck Equation, Springer 1996

Practice groups

  • Group 01 (Oliver Drozdowski)
    34 participants
    Philosophenweg 12, kHS, Wed 16:15 - 18:00
Stochastic dynamics
winter term 2021/2022
Link zum LSF
34 participants