NFYK10006U Diffusive and Stochastic Processes

Skills
At the conclusion of the course students are expected to be able to:

• Describe diffusion process using random walk, Langevin equation, and Fokker-Plank equation.
• Explain Kramars escape.
• Explain the fluctuation-dissipation theorem.
• Explain the Poisson process and the birth and death process. Use master equations to describe time evolution and steady state of the processes.
• Explain the relationship between master equations and Fokker-Plank equations.
•  Explain asymmetric exclusion process and some related models to describe traffic flow and jamming transition in one-dimensional flows.
• Apply the concepts and techniques to various examples from non-equilibrium complex phenomena.

Knowledge
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 exclusion process.

Competences
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. project.