Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models

Abstract

We consider several one-dimensional driven lattice-gas models that show a phase transition in the stationary state between a high-density fluid phase in which the typical length of a hole cluster is of order unity and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice-gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterize the scaling of the saturation width and the relaxation time of the interface with the system size are given by the Kardar-ParisiZhang exponents. However, at the critical point, we show analytically that when the equal time density-density correlation function decays slower than inverse distance, the roughness exponent varies continuously with a parameter in the hop rates but it is one half otherwise. Using these results and numerical simulations for the density-density autocorrelation function, we further find that the dynamic exponent z = 3/2 in all cases.

Critical dynamics of classical systems under slow quench

“…We study a classical nonequilibrium system in one dimension which shows a jamming transition in the stationary state [28]. The steady state of this model is known exactly [29], and some results for the coarsening dynamics [4,30] and stationary-state dynamics [31] have also been obtained. However, the dynamics of this model under slow annealing have not been studied and here we address this problem using numerical simulations.…”

“…The stationary-state dynamics have also been studied and it has been found that at the critical point, the steadystate density fluctuations decay on a time scale that grows as L z where the dynamic exponent z = 3/2 [31].…”

Critical dynamics of classical systems under slow quench

“…The steady state obeys detailed balance and is the same as that in the unidirectional model [28]. As a result, the correlation length exponent ν is given by ( 6); however, the dynamic exponent z = 2 in this case [30].…”

“…We study a classical nonequilibrium system in one dimension which shows a jamming transition in the stationary state [33]. The steady state of this model is known exactly [28], and some results for the coarsening dynamics [4,29] and stationary state dynamics [30] have also been obtained. However the dynamics of this model under slow annealing have not been studied and here we address this problem using numerical simulations.…”

“…The stationary state dynamics have also been studied and it has been found that at the critical point, the steady state density fluctuations decay on a time scale that grows as L z where the dynamic exponent z = 3/2 [30].…”