Quantum transport of non-interacting Fermi gas in an optical lattice combined with harmonic trapping

We have considered non-interacting Fermi gas in a combined harmonic and periodic potential. We calculate the energy spectrum and simulate the motion of the gas after sudden replacement of the trap centre. For different parameter regimes, the system presents dipole oscillations, damped oscillations around the replaced centre as well as localization. The behaviour can be explained by a change in the energy spectrum from linear to quadratic.