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A02 KOBAYASHI, Michikazu |Proposed Research Projects (2014-2015)

Paper | Original Paper

2015

*Daisuke Takahashi, Michikazu Kobayashi, and Muneto Nitta,
Nambu-Goldstone Modes Propagating along Topological Defects: Kelvin and Ripple Modes from Small to Large Systems,
Physical Review B 91, 184501-1-19 (2015).

[Summary] Nambu-Goldstone modes associated with (topological) defects such as vortices and domain walls in (super)fluids are known to possess quadratic/noninteger 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 wave functions ( u,v ). We find a completeagreement 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.

2014

*Michikazu Kobayashi, and Muneto Nitta,
Nonrelativistic Nambu-Goldstone Modes Associated with Spontaneously Broken Space-Time and Internal Symmetries,
Physical Review Letters 113, 120403/1-5 (2014).

[Summary] We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in nonrelativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) σ model, a magnetic domain wall in ferromagnets with an easy axis.

*Michikazu Kobayashi, and Muneto Nitta,
Nonrelativistic Nambu-Goldstone modes propagating along a Skyrmion line,
Physical Review D 90, 025010/1-9 (2014).

[Summary] We study Nambu-Goldstone (NG) modes or gapless modes propagating along a Skyrmion (lump) line in a relativistic and nonrelativistic O(3) sigma model, the latter of which describes isotropic Heisenberg ferromagnets. We show for the nonrelativistic case that there appear two coupled gapless modes with a quadratic dispersion. In addition to the well-known Kelvin mode consisting of two translational zero modes transverse to the Skyrmion line, we show that the other consists of a magnon and dilaton, that is, a NG mode for a spontaneously broken internal U(1) symmetry and a quasi-NG mode for a spontaneously broken scale symmetry of the equation of motion. We find that the commutation relations of Noether charges admit a central extension between the dilatation and phase rotation, in addition to the one between two translations found recently. The counting rule is consistent with the Nielsen-Chadha and Watanabe-Brauner relations only when we take into account quasi-NG modes.

Michikazu Kobayashi, and *Eiji Nakano, and Muneto Nitta,
Color Magnetism in Non-Abelian Vortex Matter,
Journal of High Energy Physics 6, 130/1-12 (2014).

[Summary] We propose color magnetism as a generalization of the ordinary Heisenberg (anti-)ferro magnets on a triangular lattice. Vortex matter consisting of an Abrikosov lattice of non-Abelian vortices with color magnetic fluxes shows a color ferro or anti-ferro magnetism, depending on the interaction among the vortex sites. A prime example is a non-Abelian vortex lattice in rotating dense quark matter, showing a color ferromagnetism. We show that the low-energy effective theory for the vortex lattice system in the color ferromagnetic phase is described by a 3+1 dimensional.