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A phenomenon can hardly be found that accompanied physical paradigms andtheoretical concepts in a more reflecting way than magnetism. From thebeginnings of metaphysics and the first classical approaches to magnetic polesand streamlines of the field, it has inspired modern physics on its way to theclassical field description of electrodynamics, and further to the quantummechanical description of internal degrees of freedom of elementary particles.Meanwhile, magnetic manifestations have posed and still do pose complex andoften controversially debated questions. This regards so various and utterlydistinct topics as quantum spin systems and the grand unification theory. Thismay be foremost caused by the fact that all of these effects are based oncorrelated structures, which are induced by the interplay of dynamics andelementary interactions. It is strongly correlated systems that certainlyrepresent one of the most fascinating and universal fields of research. Inparticular, low dimensional systems are in the focus of interest, as theyreveal strongly pronounced correlations of counterintuitive nature. As regardsthis framework, the quantum Hall effect must be seen as one of the mostintriguing and complex problems of modern solid state physics. Even after twodecades and the same number of Nobel prizes, it still keeps researchers ofnearly all fields of physics occupied. In spite of seminal progress, itsinherent correlated order still lacks understanding on a microscopic level.Despite this, it is obvious that the phenomenon is thoroughly fundamental ofnature. To resolve some puzzles of this nature is a key topic of this thesis.(excerpt from abstract)

Ultracold Atomic Gases in Artificial Magnetic Fields (PhD thesis)