Fermions in anisotropic harmonic trap

We study a few properties of fermions in an anisotropic harmonic trap in absence as well as in presence of an optical lattice. The density of states (DOS) and specific heat of the fermions are studied for different anisotropies. Analytical expressions for the DOS in a strongly anisotropic harmonic trap are derived. For a particular combined potential, where the fermions are hopping in a 3D lattice under a 2D harmonic potential, the Drude weight of the fermionic system is evaluated. The Drude weight is found to be flat in a wide range of fermion concentrations where it is almost temperature independent.