Abstract
Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.
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