Abstract
The asymmetric simple exclusion process (ASEP) is a paradigm for non-equilibrium physics that appears as a building block to model various lowdimensional transport phenomena, ranging from intracellular traffic to quantum dots. We review some recent results obtained for the system on a periodic ring by using the Bethe ansatz. We show that this method allows one to derive analytically many properties of the dynamics of the model such as the spectral gap and the generating function of the current. We also discuss the solution of a generalized exclusion process with N species of particles and explain how a geometric construction inspired from queuing theory sheds light on a matrix product representation technique that has been very fruitful for deriving exact results for the ASEP.
| Original language | English |
|---|---|
| Article number | P01024 |
| Journal | Journal of Statistical Mechanics: Theory and Experiment |
| Volume | 2011 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2011 |
| Externally published | Yes |
Keywords
- Exact results
- Integrable spin chains (vertex models)
- Large deviations in non-equilibrium systems
- Stochastic particle dynamics (theory)