Title: Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover,
Abstract: We discuss the derivation of a low-energy effective field theory of phase
(Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic
theory of attractive fermions. The coupled equations for Goldstone and Higgs
fields are critically analyzed in the Bardeen-Cooper-Schrieffer (BCS) to
Bose-Einstein condensate (BEC) crossover both in three spatial dimensions and
in two spatial dimensions. The crucial role of pair fluctuations is
investigated, and the beyond-mean-field Gaussian theory of the BCS-BEC
crossover is compared with available experimental data of the two-dimensional
ultracold Fermi superfluid.