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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. We study the response to both monopole and quadrupole perturbations of the trap potential and investigate the character of excitations in each case. Simple analytic formulas are provided based on the linearized scaling ansatz and accurate numerical results are obtained by satisfying the first eight moments of the CBV equation. Except for the lowest lying monopole mode that exhibits a negligible damping in all of the studied cases, the quadrupole and the higher order monopole modes undergo a transition from the collisionless regime to a highly dissipative crossover regime and finally to the hydrodynamic regime upon increasing the dipolar interaction strength. For strong vertical confinements (2D limit), we predict the existence of a temperature window within which the characteristics of the collective modes become temperature independent. This behavior, which is a unique feature of the universal near-threshold 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 in the reach of current experiments.