TY - JOUR
T1 - Condensation in the Zero Range Process
T2 - Stationary and Dynamical Properties
AU - Großkinsky, Stefan
AU - Schütz, Gunter M.
AU - Spohn, Herbert
N1 - Funding Information:
S.G. acknowledges the support of the Graduiertenkolleg ‘‘Mathematik im Bereich ihrer Wechselwirkung mit der Physik’’ and the support of the DAAD/CAPES program ‘‘PROBRAL.’’ He is also grateful for a fruitful research visit at the ‘‘Forschungszentrum Jülich,’’ where this work was initiated.
PY - 2003/11
Y1 - 2003/11
N2 - The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.
AB - The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.
KW - Equivalence of ensembles
KW - Nonequilibrium phase transition
KW - Relative entropy
KW - Zero range process
UR - http://www.scopus.com/inward/record.url?scp=0346493090&partnerID=8YFLogxK
U2 - 10.1023/A:1026008532442
DO - 10.1023/A:1026008532442
M3 - Article
AN - SCOPUS:0346493090
SN - 0022-4715
VL - 113
SP - 389
EP - 410
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3-4
ER -