Exact Solution of Asymmetric Diffusion With N Classes of Particles of Arbitrary Size and Hierarchical Order

The exact solution of the asymmetric exclusion problem with N distinct classes of particles (c = 1,2,…,N), with hierarchical order is presented. In this model the particles (size 1) are located at lattice points, and diffuse with equal asymmetric rates, but particles in a class c do not distinguish those in the classes c’ >c from holes (empty sites). We generalize and solve exactly this model by considering the molecules in each distinct class c =1,2,…,N with sizes s_c (s_c = 0,1,2,…), in units of lattice spacing. The solution is derived by a Bethe ansatz of nested type.