For the past two decades harmonically trapped ultracold atomic gases have been used with great success to study fundamental many-body physics in a flexible experimental setting. Recently, we achieved the first atomic Bose-Einstein condensate in an essentially uniform potential of an optical-box trap , which has opened new possibilities for closer connections with condensed-matter systems and theories of the many-body problem that generally rely on the translational symmetry of the system. I will present two directions that we have recently explored with this new system: the (Kibble-Zurek) dynamics of spontaneous symmetry breaking in a quenched homogeneous gas , and the emergence of turbulence in a periodically driven quantum gas.
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