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Flavor Degeneracy and Effects of Disorder in Ultracold Atom Systems

Cold atoms in optical lattices offer an exciting new laboratory where quantum many-body phenomena can be realized in a highly controlled way. They can even serve as quantum simulators for notoriously difficult problems like high-temperature superconductivity. This review is focussed on recent developments and new results in multi-component systems. Fermionic atoms with SU(N) symmetry have exotic superfluid and flavor-ordered ground states. We discuss symmetry breaking, collective modes and detection issues. Bosonic multi-flavor ensembles allow for engineering of spin Hamiltonians which are interesting from a quantum computation point of view. Finally, we will address the competition of disorder and interaction in optical lattices. We present a complete phase diagram obtained within dynamical mean-field theory and discuss experimental observability of the Mott and Anderson phases.