2003/07/28 by K. Krebs, K Krebs, F. H. Jafarpour +3 · 7 citations
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1367-2630/5/1/145
published as New J. Phys. {\bf 5}, 145.1-145.14 (2003) · 27 pages
arxiv created 2003/07/28 · openalex publication_date 2003/10/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
We obtain exact travelling wave solutions for three families of stochastic one-dimensional non-equilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) shocks in the partially asymmetric exclusion process with open boundaries, (ii) a lattice Fisher wave in a reaction–diffusion system, and (iii) a domain wall in non-equilibrium Glauber–Kawasaki dynamics with magnetization current. For each of these systems we define a microscopic shock position and calculate the exact hopping rates of the travelling wave in terms of the transition rates of the microscopic model. In the steady state a reversal of the bias of the travelling wave marks a first-order non-equilibrium phase transition, analogous to the Zel'dovich theory of kinetics of first-order transitions. The stationary distributions of the exclusion process with n shocks can be described in terms of n -dimensional representations of matrix product states.