| Abstract: | The asymmetric simple exclusion process (ASEP) can be solved exactly
using integrability techniques borrowed from the theory of quantum
integrable systems. This model can be used as a template to study various
aspects of non-equilibrium statistical physics. In particular, we
shall show how spectral properties of the evolution matrix, current
fluctuations and mappings to vertex models can be understood with the
help of coordinate and functional Bethe Ansatz. These technical tools
allow us to calculate large deviation functions of currents
and density profiles, that generalize the thermodynamic potentials
to non-equilibrium situations.
We shall also discuss extensions of this model that involve different species of particles with hierarchical dynamical rules. We shall show that the exact solutions of these generalized models are based upon representations of quadratic algebras. |
