%0 Generic
%A Plötz, Patrick
%D 2010
%F heidok:11123
%K Komplexe Dynamik , Kalte Atome , Bandkopplung , Hubbard-Modellcomplex dynamics , cold atoms , band coupling , Hubbard model
%R 10.11588/heidok.00011123
%T Complex Dynamics of Ultracold Atoms
%U https://archiv.ub.uni-heidelberg.de/volltextserver/11123/
%X Motivated by current experiments with ultracold atoms, the study of complex dynamics of Bose-Einstein condensates in optical lattices forms the central subject of this work. A lattice model of interacting bosons under the influence of an external force is motivated and derived from the experimental setup. Several dynamical regimes of this model are discussed in this thesis. In a first part we will develop a new measure for detecting avoided crossings in complex energy spectra and apply it to the quantum chaotic regime of the single-band system. The second and main part of this work is dedicated to the coupling between energy bands described in terms of a two-band model. The complex time evolution is already apparent in the horizontal and vertical population dynamics of the non-interacting problem. We find resonances in the interband transport, and, in a second step, study the effect of  inter-particle interactions on these resonant oscillations. We are able to predict all time scales of the complex interband dynamics even in the presence of interactions. This is possible via the introduction of an effective model that is motivated and supported by a multitude of numerical results and proves exactly solvable.