Nambu-Goldstone bosons with fractional-power dispersion relations

Abstract

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.

Comments: 5 pages, 1 figure. v2: references added; published version