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

TL;DR

This paper investigates the slow decay of autocorrelation functions in a complex deposition-evaporation model with many conservation laws, revealing diverse decay behaviors linked to diffusion processes and interface roughening.

Contribution

It introduces a model with multiple conservation laws exhibiting varied autocorrelation decay patterns and relates these to diffusion of labeled particles and interface dynamics.

Findings

Autocorrelation decays as different powers or as exp(-t^{1/2}) depending on sector.

Dynamical exponent z is approximately 2.55 in the empty line sector.

Model generalizes the KPZ interface roughening framework.

Abstract

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 $\exp (-t^{1/2})$, 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 $2.55 \pm 0.15$.