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We investigate the time evolution of wave packets in systems with a mixedphase space where regular islands and chaotic motion coexist. For wave packetsstarted in the chaotic sea on average the weight on a quantized torus of theregular island increases due to dynamical tunneling. This flooding weightinitially increases linearly and saturates to a value which varies from torusto torus. We demonstrate for the asymptotic flooding weight universal scalingwith an effective tunneling coupling for quantum maps and the mushroombilliard. This universality is reproduced by a suitable random matrix model.

Temporal flooding of regular islands by chaotic wave packets