I will start with a brief introduction to a one-dimensional nonequilibrium model called the exclusion process in which a hard-core particle hops to the empty nearest neighbor at a specific rate. Variants of the exclusion process are widely used to understand traffic flow in many realistic systems like vehicular flow, molecular motors, ant trails, etc. In my talk, I will discuss some variants of the model that undergo a non-trivial jamming transition at the finite critical point and explore some of their key properties.
I will then present some exact and interesting results for the two-point steady state correlation function at the critical point, followed by results on the autocorrelation function, derived using the hydrodynamic equation.
Here is a video that covers a few scenarios of jamming in vehicular traffic flow: