Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Poster II
DY 29.11: Poster
Donnerstag, 28. Februar 2008, 16:00–18:00, Poster C
Diffusion and dissipation in complex quantum systems — •Dominik Samson and Heiko Rieger — Theoretische Physik, Universität des Saarlandes, PF 151150, D-66041 Saarbrücken
The Hamiltonian of a quantum-mechanical system contains a time-dependent parameter X. The system is prepared in a highly excited eigenstate of the instantaneous Hamiltonian, and we compute the amplitudes <n(t)|φ(t)> to be in the eigenstates |n> of the instantaeous Hamiltonian H(X(t)) at later times. It was already found for generic Systems that the occupation probability spreads diffusively away from the initial state [1]. The diffusion constant D is now investigated numerically in random matrix models (GOE and GUE) as a function of Ẋ. We are able to prove numerically the theoretical predictions in two limiting regimes of both matrix models: in the GOE case, we have two D(Ẋ) behaviours, in the GUE case D has an unitarity dependence, always corresponding to Ohmic dissipation predicted by the Kubo formula and Landau-Zener transitions. We also study the sample to sample fluctuation of energy, Δ E=<[E(t)−E(t=0)]2> in both ensembles, which seems to have a sub-ohmic behaviour.
[1] Michael Wilkinson, Diffusion and dissipation in complex quantum systems, Phys. Rev. A 41, 4645 (1990)