Stochastic descriptions offer powerful ways to understand
fluctuating and noisy phenomena, and are widely used in many
scientific discipline including physics, chemistry, and biology. In
this course, basic analytical and numerical tools to analyze
stochastic phenomena are introduced and will be demonstrated on
several important natural examples. Students will learn to master
stochastic descriptions for analyzing non-equilibrium complex
At the conclusion of the course students are expected to be able
Describe diffusion process using random walk, Langevin
equation, and Fokker-Plank equation.
Explain the first passage time and Kramers escape problem
Explain the fluctuation-dissipation theorem.
Explain basic concepts in stochastic integrals.
Explain the Poisson process and the birth and death process.
Use master equations to describe time evolution and steady state of
Explain the relationship between master equations and
Fokker-Plank equations using Kramas-Moyal expansion and the linear
Explain asymmetric simple exclusion process and some
related models to describe traffic flow and jamming transition in
Apply the concepts and techniques to various examples from
non-equilibrium complex phenomena.
In this course, first basic tools to analyse stochastic phenomena
are introduced by using the diffusion process as one of the most
useful examples of stochastic process. The topics include random
walks, Langevin equations, Fokker-Planck equations, Kramars escape,
and the fluctuation-dissipation theorem. Then selected stochastic
models that have wide applications to various real phenomena are
introduced and analysed. The topics are chosen from non-equilibrium
stochastic phenomena, including birth and death process and Master
equation, and asymmetric simple exclusion process. Throughout the
course, exercises for analytical calculations and numerical
simulations are provided to improve the students' skills.
This course will provide the students with mathematical tools that
have application in range of fields within and beyond physics.
Examples of the fields include non-equilibrium statistical physics,
biophysics, soft-matter physics, complex systems, econophysics,
social physics, chemistry, molecular biology, ecology, etc.
This course will provide the students with a competent background
for further studies within the research field, i.e. a M.Sc.
Teaching and learning methods
Lectures and exercise sessions. Computer exercise
Equilibrium statistical physics, physics bachelor
level mathematics (Especially: differential and integral calculus,
differential equations, Taylor expansions).