Nambu-Goldstone bosons with fractional-power dispersion relations
  We pin down the origin of a peculiar dispersion relation of domain wall fluctuation, the so-called ripplon, in a superfluid-superfluid interface. A ripplon has a dispersion relation $\omega\propto k^{3/2}$ due to the nonlocality of the effective Lagrangian, which is mediated by gapless superfluid phonons in the bulk. We point out the analogy to the longitudinal phonon in the two-dimensional Wigner crystal. 
Haruki Watanabe, Hitoshi Murayama
hep-th cond-mat.other hep-ph