Interacting Two-Particle Discrete-Time Quantum Walk with Percolation

We investigate discrete-time quantum walk of two interacting particles on one-dimensional percolation lattice. The dynamical percolation can make the quantum walk diffuse classically while the static percolation can make it localize at the neighbor of the initial site. According to the symmetry for two bosons, fermions and classical indistinguishable particles, three kind of initial states are considered. The interaction between two particles leads to bosons anti-bunching and fermions bunching. We focus on the joint probability distributions, the average distance and the meeting probability to describe the global properties of quantum walk. The joint probability distributions of two particles spread more out over the walking region in the dynamical percolation, while they are concentrated on the neighbor of the initial position in the statical case. For fermions and bosons initial states, both the curves of the meeting probability and that of the average distance occur crossing at a certain value of percolation probability, which is a result induced by the interplay between the interaction and percolation.