Anomalous transport and first-passage statistics of run-and-tumble particles with repeated trapping in disordered media

Abstract: We investigate anomalous transport and first-passage properties of run-and-tumble particles in disordered environments using a generalized renewal framework that decouples directional persistence from stochastic trapping. Unlike standard models, multiple trapping events may occur within a single run without resetting orientation. Run and trapping times are drawn from exponential or power-law distributions, enabling both Markovian and non-Markovian regimes. Exponential statistics yield ergodic ballistic-to-diffusive crossover dynamics, whereas power-law trapping (1<α<2) induces subdiffusion and weak ergodicity breaking, and power-law runs (1<β<2) produce superdiffusive transport. Their interplay generates a continuum of anomalous scaling regimes and a diffusive crossover near α+β≈3.5. Despite heavy-tailed dynamics, confinement regularizes first-passage statistics, ensuring finite mean first-passage times. These results establish a minimal stochastic framework for intermittently hindered active transport and provide quantitative predictions for scaling behavior and search efficiency in heterogeneous media. Graphic abstract: (Figure presented.)