Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Quantum chaos II

DY 25.1: Invited Talk

Thursday, March 29, 2007, 09:30–10:00, H2

Surprises in the time-evolution of wave-packets — •Arnd Bäcker — Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany

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 is explained in terms of the eigenstates [1] and with a random matrix model. One interesting application are rough nano-wires in a magnetic field where surprisingly large localization lengths can be understood by this flooding process [2].

[1] A. Bäcker, R. Ketzmerick, and A. Monastra, Phys. Rev. Lett. 94 054102 (2005).

[2] J. Feist, A. Bäcker, R. Ketzmerick, S. Rotter, B. Huckestein, and J. Burgdörfer, Phys. Rev. Lett. 97 116804 (2006).