Boyka Aneva (INRNE, Bulgarian Academy of Sciences, Sofia, Bulgaria)

Quantum symmetries and exactly solvable models of nonequilibrium physics

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.