Exclusion process for particles of arbitrary extension : Hydrodynamic limit and algebraic properties

The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called ℓ-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary length ℓ. Stationary and dynamical properties of the ℓ-ASEP with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the underlying stochastic many-body system. In particular, the hydrodynamic equation for the local density evolution and the time-dependent diffusion constant of a tracer particle are calculated. As a fundamental algebraic property of the symmetric exclusion process (SEP) the SU (2)-symmetry is generalized to the case of extended particles.