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 $ω\propto k^{3/2}$ 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.

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