Mean path length invariance in wave-scattering beyond the diffusive regime

Diffusive random walks feature the surprising property that average length of all possible trajectories enter and exit a finite domain is determined solely by boundary. Changes in diffusion constant or mean-free path, characterize process, leave mean path unchanged. Here we demonstrate experimentally this result can be transferred to scattering waves, even when wave interference leads marked deviations from process. Using versatile microwave setup, establish invariance for crossover Anderson localization case band gap photonic crystal. We obtain these results on based transmission matrix measurement through novel procedure turns out more robust absorption incomplete localized regime as compared an assessment full matrix.