Limiting distributions of ergodic continuous-time quantum walks on periodic graphs
Anne Boutet de Monvel, Kiran Kumar A. S., Mostafa Sabri · arXiv (Cornell University) · 2025
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk explicitly. We uncover interesting behavior where in some families, the walk is ergodic in both horizontal and sectional directions, while in others, ergodicity only holds in the horizontal (large N) direction. We compare this to the limiting distribution of classical random walks on the same graphs.