Semi-open boundary for random walking shocks

Abstract

Non-stationary time evolution of interacting particle systems is in general a rather difficult topic however, exceptional examples are known where hidden processes within the model make the description manageable. These hidden processes often take the form of a finite number of interacting random walks and in some cases, rather than being hidden, were very explicitly revealed as second class particles associated with the model. The examples of asymmetric exclusion and exponential bricklayers model are known in this context, where such distributional structure was demonstrated in infinite volume. Here we find boundary mechanisms that save this remarkable structure in finite volume of the model with semi-open boundaries that let ordinary particles, but not the shocks, through. This finding also allows to characterise nontrivial two-species, non-reversible stationary distributions subject to our special boundary rates.