Slow Relaxation in a Model with Many Conservation Laws: Deposition and Evaporation of Trimers on a Line

We study the slow decay of the steady-state autocorrelation function $C(t)$ in a stochastic model of deposition and evaporation of trimers on a line with infinitely many conservation laws and sectors. Simulations show that $C(t)$ decays as different powers of t, or as exp(-t1/2), depending on the sector. We explain this diversity by relating the problem to diffusion of hard core particles with conserved spin labels. The model embodies a matrix generalization of the Kardar-Parisi-Zhang model of interface roughening. In the sector which includes the empty line, the dynamical exponent z is 2.55 ±{} 0.15.