Dresden 2011 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 12: Quantum Dynamics, Decoherence, and Quantum Information II
DY 12.6: Vortrag
Dienstag, 15. März 2011, 11:30–11:45, ZEU 255
Quantum dynamics of the time-dependent elliptical billiard — •Florian Lenz1, Fotis K. Diakonos2, and Peter Schmelcher1 — 1Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg — 2Department of Physics, University of Athens, GR-15771 Athens, Greece
We analyze the quantum dynamics of the time-dependent elliptical billiard. Since there are no standard methods available to tackle this problem, a numerical procedure for the time-propagation of an arbitrary initial state is developed. To circumvent the time-dependent Dirichlet boundary conditions, a series of transformations is applied, yielding a Hamiltonian with static boundary conditions but in turn time-dependent masses and additional time-dependent potential terms. By means of an expansion ansatz, this eventually yields a large system of coupled ordinary differential equations, which can be solved by standard techniques. While for low driving frequencies the evolution of the energy is purely adiabatic, with increasing frequency more and more higher excited states with the same symmetry properties as the initial state get populated. The time-evolution of the population coefficients of the instantaneous eigenstates exhibit characteristic periods, which are much larger than the period of the external driving. These periods depend sensitively on the driving frequency and display a resonance like structure. We employ a Rabi-like coupled, driven few level model to trace the origin of the large periods of the population coefficients and find excellent agreement with the full numerical simulations.