A series of 4 lectures (on January 25, January 27, February 3 and February 4).
The lectures will be at the level of a graduate student.
Exclusion processes are very simple lattice gas models which are fundamental models of many-particle stochastic dynamics and nonequilibrium phenomena. In these lectures I will describe an important an important example, the asymmetric exclusion process with
open boundaries, and show how nonequilibrium phase transitions come about in this one-dimensional system. I will show how the nonequilibrium stationary state may be solved exactly as a matrix product state. Generalisations to multi species processes which give rise to tensor product states will also be discussed.
Provisional Plan:
I Asymmetric Exclusion Process with open boundaries:phase diagram and mean field theory
II Exact solution : matrix product stationary state
III Nonequilibrium partition function: Yang-Lee zeros; static and dynamic phase transitions
IV Multispecies generalisations: tensor product States and relation to queueing theory
