 9257 Alexander Francis J., Cheng Zheming , JanowskySteven A., Lebowitz Joel L.
 Shock Fluctuations in the TwoDimensional Asymmetric
Simple Exclusion Process
(404K, LaTeX)
May 15, 92

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We study via computer simulations (using various serial and parallel
updating techniques) the time evolution of shocks, particularly the
shock width $\sigma(t)$, in several versions of the twodimensional
asymmetric simple exclusion process (ASEP). The basic dynamics of this
process consists of particles jumping independently to empty neighboring
lattice sites with rates $p_{\rm up} = p_{\rm down} = p_\perp$, $p_{\rm
left} < p_{\rm right}$. If the system is initially divided into two
regions with densities $\rho_{\rm left} < \rho_{\rm right}$, the
boundary between the two regions corresponds to a shock front.
Macroscopically the shock remains sharp and moves with a constant
velocity $v_{\rm shock} = (p_{\rm right}  p_{\rm left})(1  \rho_{\rm
left}  \rho_{\rm right})$. We find that microscopic fluctuations cause
$\sigma$ to grow as $t^\beta$, $\beta\approx 1/4$. This is consistent
with theoretical expectations.
We also study the nonequilibrium stationary states of the ASEP on a
periodic lattice, where we break translation invariance by reducing the
jump rates across the bonds between two neighboring columns of the
system by a factor $r$. We find that for fixed overall density
$\rho_{\rm avg}$ and reduction factor $r$ sufficiently small (depending
on $\rho_{\rm avg}$ and the jump rates) the system segregates into two
regions with densities $\rho_1$ and $\rho_2=1\rho_1$, where these
densities do not depend on the overall density $\rho_{\rm avg}$. The
boundary between the two regions is again macroscopically sharp. We
examine the shock width and the variance in the shock position in the
stationary state, paying particular attention to the scaling of these
quantities with system size. This scaling behavior shows many of the
same features as the timedependent scaling discussed above, providing
an alternate determination of the result $\beta\approx 1/4$.
 Files:
9257.src(
desc ,
9257.tex )