TY - JOUR
T1 - Dynamical transition in the TASEP with Langmuir kinetics: Mean-field theory
AU - Botto, Davide
AU - Pelizzola, Alessandro
AU - Pretti, Marco
AU - ZAMPARO, MARCO
PY - 2019
Y1 - 2019
N2 - We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation rate of the system toward its non-equilibrium steady state. In the high-density (low-density) phase, the relaxation rate becomes independent of the injection (extraction) rate at a certain critical value of the parameter itself, and this transition is not accompanied by any qualitative change in the steady-state behavior. We characterize the relaxation rate by means of bounds, becoming tight in the thermodynamic limit. These results are generalized to the TASEP with Langmuir kinetics, where particles can also bind to empty sites or unbind from occupied ones in the symmetric case of equal binding/unbinding rates. The theory predicts that a dynamical transition will occur in this case as well.
AB - We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation rate of the system toward its non-equilibrium steady state. In the high-density (low-density) phase, the relaxation rate becomes independent of the injection (extraction) rate at a certain critical value of the parameter itself, and this transition is not accompanied by any qualitative change in the steady-state behavior. We characterize the relaxation rate by means of bounds, becoming tight in the thermodynamic limit. These results are generalized to the TASEP with Langmuir kinetics, where particles can also bind to empty sites or unbind from occupied ones in the symmetric case of equal binding/unbinding rates. The theory predicts that a dynamical transition will occur in this case as well.
UR - https://iris.uniupo.it/handle/11579/173842
U2 - 10.1088/1751-8121/aaf1f8
DO - 10.1088/1751-8121/aaf1f8
M3 - Article
SN - 1751-8113
SP - 045001
JO - JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
JF - JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
ER -