Statics and Dynamics of Exclusion Processes

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