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Abstract

This thesis explores the dynamics and especially the low-energy spectra of Bose-Einstein condensates (BECs) in one- and two-dimensional potential traps. Of particular interest are many-body effects. To obtain numerically exact results for the dynamics, the well-established multiconfigurational time-dependent Hartree for bosons (MCTDHB) method is applied. Excited states are calculated utilizing the recently introduced linear-response theory atop it (LR- MCTDHB). The core of the latter theory is an in general non-hermitian eigenvalue problem. The newly developed implementation of this theory is described in detail and benchmarked towards the exactly-solvable harmonic-interaction model. Several applications are discussed. With respect to dynamics, it is shown that both the out-of-equilibrium tunneling dynamics and the dynamics of trapped vortices are of many-body nature. Furthermore, many-body effects in the excitation spectra are presented for BECs in different trap geometries. It is demonstrated that even for essentially-condensed systems, the spectrum of the lowest-in-energy excitations computed at the many-body level differs substantially from a standard mean-field description. In general, it is shown that bosons carrying angular momentum are more sensitive to many-body effects, both in the dynamics and the excitation spectrum.