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 $C\left(t\right)\mathrm{}$ in a stochastic model of deposition and evaporation of trimers on a line with infinitely many conservation laws and sectors. Simulations show that $C\left(t\right)\mathrm{}$ decays as different powers of $t$, or as $\exp \left({-t}^{\frac{1}{2}}\right)$, 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.