Ballistic Speed and Potential-Theoretic Recurrence for Homogeneous Open Quantum Random Walks
The study connects macroscopic ballistic transport (RMS speed) to microscopic recurrence properties in finite-range open quantum random walks. It proves that for homogeneous walks, RMS speed equals drift norm, indicating transience if there is a nonzero drift. A crucial finding is the drift-dimension dichotomy: recurrent at the origin in effective dimensions one or two without a drift, but spatially transient in three or higher dimensions.