Majorana random walks with braiding

The field of statistical mechanics has a long history of studying random walks. Usually, the random walkers are endowed with classical properties, such as their diffusion rate or some aggregation or annihilation rules based on the identity of the walker. A natural generalization of such a system is to allow some of these properties to be quantum mechanical in nature. In this talk, we will present a model of Majorana fermions which are allowed to perform classical random walks in 1+1D, but have local rules for interactions which account for the highly non-local nature of Majorana fermions. In particular, we will present exact results which demonstrate that the interplay of braiding and pairwise annihilation processes of Majorana fermions gives rise to a robust universality class of non-equilibrium, semi-classical systems.