| Summary: | This thesis consists of two projects which are seemingly disconnected, yet closely related. The first part explores the effects of Bose-Einstein condensation at temperatures close to, but slightly above, criticality. Following a general introduction into bosonic condensation we justify why a phenomenological theory, similar to the Ginzburg-Landau theory for fermions, holds for weakly interacting Bose gases. From this theory we predict the divergence of certain observables, in particular the quasi-magnetic susceptibility, and discuss the effects of a trapping potential. The divergence of the magnetic susceptibility motivates the introduction of an original scheme in order to measure it, published in Phys. Rev. A 93, 041602(R). The scheme uses modulated laser fields to create well- controlled gradients of artificial magnetic fields. In addition we discuss how rotational schemes might be helpful in detecting different quantum phases by exploiting different signatures in their moments of inertia. The second part investigates binary mixtures in one dimension. We show that in certain limits such systems behave like two simply coupled Luttinger liquids, which effectively describe polaronic modes. We study and calculate explicitly how an impurity immersed in the one dimensional system creates two depletion clouds and a phase drop in each of the liquids. After arguing that these clouds and phase drops necessitate a coupling of the impurity to the low-lying excitation modes of the Luttinger liquids, we derive the edge-state singularities of the bosonic and fermionic dynamical structure factors which depend on the coupling between the liquids.
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