Transport of fermions in an optical lattice
Optical lattices present an opportunity to study the Fermi-Hubbard model at moderate temperature without the complications of phonons or disorder that would be found in typical materials. Instead, atom-atom scattering plays the dominant role inhibiting mass transport. In a recent experiment, ultracold 40K atoms are loaded into a three-dimensional (3D) lattice with a low filling factor, allowing investigation of their transport properties. We solve the Boltzmann equation with a particular Ansatz (close to what is done in hydrodynamics) to find a damped-oscillator equation for the centre of mass of the atoms, along with a closed-form expression for the rate of current dissipation. This approach is then compared to the experimental results, and we find a fair agreement without any fitting parameter. In the last part of the talk, the Fermi Liquid low temperature behaviour of the dissipation rate is explored. The effect of spatial dimension is also investigated in 2D, 3D, and infinite dimensional lattices.

