Quantum symmetries and exactly solvable models of nonequilibrium physics

Abstract:
We consider driven diffusive systems on one dimensional lattice as models of nonequilibrium physics. These systems provide a very good playground to enhance utility of quantum group symmetries. The deformation parameter has a direct physical meaning - it is the ratio of left/right diffusion rates. We apply an approach inspired by the inverse scttering method where the stationary probability distribution is expressed in terms of noncommutative matrices that form a comodule of SU_q(n) and this is the model bulk symmetry. Boundary processes amount to a reduction of the bulk symmetry. We argue that for open systems the boundary operators generate a tridiagonal algebra whose irriducible representations are given by the Askey-Wilson polynomials and allow to solve the model exactly.