Time-reversed imaging as a diagnostic of wave and particle chaos

In the presence of multiple scattering, waves and particles behave fundamentally differently. As a model for the stability of the temporal evolution of particle and wave propagation, a scattering system is presented in which particle propagation is strongly unstable while wave propagation is significantly more stable. Both analytical and numerical evidence for the different stability properties of wave and particle propagation is presented; the exponential divergence of particle trajectories leads to a critical length scale for the stability of particle propagation that depends exponentially on time $\left[\exp \right(-\mu t\left)\right],$ whereas the critical length scale for the stability of wave propagation decreases with time only as $1/\sqrt{t}.$ This fundamental difference is due to wave suppression of classical chaos that is intimately related to the concept of ray splitting.