| Ultracold atoms in optical lattices provide ideal realizations of one of the most important models for correlated quantum systems, the Hubbard model. The tunability of these systems allows to explore new effects beyond the thermal equilibrium. Motivated by recent experiments, we investigate several simple examples for this. For example, we find that the expansion of atomar clouds in optical lattices is governed by the crossover from diffusive to ballistic behavior and that a pure hydrodynamic description breaks down due to the singular nature of the relevant diffusion equations. We also discuss how and on what time scales negative absolute temperatures can be established in simple experimental setups. Furthermore, we investigate some unexpected properties of the Hubbard model in a constant electric or gravitational field, where only interactions allow an atomar cloud to expand. |
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