Quantum percolation theory for dynamic propagation connectivity of transport networks

Abstract

Connectivity degradation in transport networks under structural disturbance is a central problem in network resilience research. Existing methods rely mainly on percolation theory and topological connectivity measures. They focus on whether paths exist and whether connected components fragment. These approaches cannot capture functional degradation where network topology remains intact but propagation ability has already declined substantially. This paper introduces quantum percolation theory into transport network connectivity analysis and proposes Dynamic Propagation Connectivity (DPC) as a new measure that characterises network propagation ability under disturbance. By mapping a transport network under disturbance into a propagation operator system, this paper establishes a spectral analysis framework for DPC and defines the time-averaged participation index as its core quantification. This paper provides a series of rigorous theoretical results. DPC remains constant under homogeneous disturbance and degrades under heterogeneous disturbance. This paper establishes a quantitative relationship between the degradation rate, the minimum eigenvalue spacing of the propagation operator, and heterogeneous deviation strength. This paper proves a separation theorem between DPC and algebraic connectivity. It derives an analytical expression for DPC and a second-order perturbation approximation on the ring graph. Numerical experiments on three transport benchmark networks verify all theoretical conclusions and confirm degradation monotonicity, separation from algebraic connectivity, and degradation amplification by network size. This paper provides a theoretical framework for transport network resilience assessment that goes beyond topological connectivity.