Relaxation time in a non-conserving driven-diffusive system with   parallel dynamics
  We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit. 
S. R. Masharian, F. H. Jafarpour and A. Aghamohammadi
cond-mat.stat-mech