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

We consider a 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 center. For different parameter regimes, the system presents dipole oscillations, damped oscillations around the replaced center, and localization. The behaviour is explained by the change of the energy spectrum from linear to quadratic.