Collective excitations of quasi-two-dimensional trapped dipolar fermions: Transition from collisionless to hydrodynamic regime

We study the collective excitations of polarized single-component quasi-two-dimensional dipolar fermions in an isotropic harmonic trap by solving the collisional Boltzmann-Vlasov (CBV) equation via the method of moments. We study the response to monopole and quadrupole perturbations of the trap potential and investigate thedynamicalcharacterofexcitationsineachcase.Simpleanalyticformulasarefoundusingthelinearizedscaling ansatzapproximationandaccuratenumericalresultsareobtainedbysatisfyingthefirsteightmomentsoftheCBV equation. Except for the lowest-lying monopole mode that is weakly affected by collisions, the quadrupole and the higher-order monopole modes undergo a transition from the collisionless regime to a dissipative crossover regime and finally approach the hydrodynamic regime upon increasing the dipolar interaction strength. For strong transverse confinement (2D limit), we predict the existence of a temperature window within which the characteristics of the collective modes become temperature independent. This plateau, which is a direct consequence of dipole-dipole scatterings, persists as long as the scattering energies remain in the near-threshold regime. The predictions of this work are expected to be observable in the current experiments.