Illinois PHYS 466, Lecture 13: Brownian Dynamics

By David M. Ceperley

University of Illinois at Urbana-Champaign

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Brownian Dynamics

Let’s explore the connection between Brownian motion and Metropolis Monte Carlo. Why?

  • Connection with smart MC
  • Introduce the idea of kinetic Monte Carlo
  • Get rid of solvent degrees of freedom and have much longer time steps.


  • Local Markov process
  • General Form of Evolution
  • Moment Expansion
  • Trotter’s formula
  • Generalized Trotter Formula
  • Evaluation of diffusion term
  • Green’s function for a gradient
  • Summary of Brownian Dynamics
  • Hydrodynamical effects
  • Langevin Equation
  • Dissipative Particle Dynamics (DPD)FS 465


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Researchers should cite this work as follows:

  • David M. Ceperley (2009), "Illinois PHYS 466, Lecture 13: Brownian Dynamics,"

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