Spectrum of Goldstone modes in Larkin-Ovchinnikov-Fulde-Ferrell superfluids

As a consequence of the continuous translational symmetry breaking, nonuniform Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) superfluids possess a rich spectrum of low-energy bosonic excitations. These excitations, which are gapless due to the Goldstone theorem, aremixtures of phase fluctuations and elastic phonon-like deformations of the order parameter. We derive microscopically the effective Gaussian action of the LOFF Goldstone modes and calculate their dispersion in the long-wavelength limit.