Hamiltonian systems show a large variety of dynamical behaviour ranging from integrable over mixed to fully chaotic dynamics. Quantum mechanically this is reflected in the properties of eigenfunctions and eigenvalue statistics. In this talk the quantum-to-classical correspondence is investigated using the time evolution of wave-packets. While classical and quantum dynamics coincide at short times, the question is what happens at larger times? For fully chaotic systems one expects that an initially localized wave-packet becomes random for sufficiently long times. It is shown that this randomization time-scale is surprisingly large.
For systems with a mixed phase space it turns out that a wave-packet, initially placed in the chaotic sea, may ignore the classical phase space boundaries and that the randomized wave-packet substantially floods into the region of the regular island. This can be understood in terms of the eigenstates and with a random matrix model. One interesting application are rough nano-wires in a magnetic field where surprisingly large localization lengths is explained in terms of this flooding process.
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