Nambu-Goldstone Modes Propagating along Topological Defects: Kelvin and Ripple Modes from Small to Large Systems

Abstract

Nambu-Goldstone modes associated with (topological) defects such as vortices and domain walls in (super)fluids are known to possess quadratic/non-integer dispersion relations in finite/infinite-size systems. Here, we report interpolating formulas connecting the dispersion relations in finite- and infinite-size systems for Kelvin modes along a quantum vortex and ripplons on a domain wall in superfluids. Our method can provide not only the dispersion relations but also the explicit forms of quasiparticle wavefunctions $(u,v)$. We find a complete agreement between the analytical formulas and numerical simulations. All these formulas are derived in a fully analytical way, and hence not empirical ones. We also discuss common structures in the derivation of these formulas and speculate on the general procedure.

20 pages, 12 figures, 1 table, final version published in Phys. Rev. B

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Cited by in corpus (7)

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• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
• The Rayleigh-Taylor instability in a binary quantum fluid
• Semiclassical dynamics of a dark soliton in a one-dimensional bosonic superfluid in an optical lattice
• Magnetic D-brane solitons: skyrmion strings ending on a Néel wall in chiral magnets
• Kelvin wave in miscible two-component Bose-Einstein condensates
• Density of condensate of a dilute Bose gas in improved Hartree-Fock approximation