Critical behavior of jamming transition in one-dimensional nonequilibrium models

Abstract

Statisticalmechanics is an essential tool to describe the behavior of complex systems ranging frombacterial growth to universe expansion. For a systemin equilibrium, this approach is well established and the stationary state distribution is given by the Boltzmann weight. Nonequilibrium systems are much more common than the equilibrium ones but a complete formalism analogous to equilibrium statistical mechanics has not been developed for nonequilibrium processes. We therefore study some simple nonequilibrium models in detail to gain an insight in these systems. In this thesis, we focus on one-dimensional nonequilibrium interacting particle systems which are driven by an external force. Such systems can show a non-trivial phase transition even in one-dimension and we are interested in understanding the critical behavior of these systems. The models studied in this thesis aremotivated by the common phenomenon of jamming that occurs in traffic flow of vehicles,molecularmotors, fluid flow through narrow pipe, etc. In this thesis, we study two generic classes of one-dimensional stochastic models: (a) lattice gasmodels of hard core particles in which a particle hops to an empty site according to the hop rule assigned to it and (b)mass transportmodels in which each site can contain many particles and a particle hops to another site according to the prescribed rule. Below we list four lattice gas models that we have worked on in this thesis and their correspondence to themass transportmodels: