We study the non-equilibrium dynamics of cold atoms held in an optical lattice potential. The expansion of an initially confined atom cloud occurs in two phases: an initial quadratic expansion followed by a ballistic behaviour at long times. Accounti
ng for this gives a good description of recent experimental results, and provides a robust method to extract the effective intersite tunneling from time-of-flight measurements.
Bose-Einstein condensates subject to short pulses (`kicks) from standing waves of light represent a nonlinear analogue of the well-known chaos paradigm, the quantum kicked rotor. Previous studies of the onset of dynamical instability (ie exponential
proliferation of non-condensate particles) suggested that the transition to instability might be associated with a transition to chaos. Here we conclude instead that instability is due to resonant driving of Bogoliubov modes. We investigate the excitation of Bogoliubov modes for both the quantum kicked rotor (QKR) and a variant, the double kicked rotor (QKR-2). We present an analytical model, valid in the limit of weak impulses which correctly gives the scaling properties of the resonances and yields good agreement with mean-field numerics.
