Interpolating relativistic and non-relativistic Nambu-Goldstone and Higgs modes

When a continuous symmetry is spontaneously broken in non-relativistic theories, there appear Nambu-Goldstone (NG) modes, whose dispersion relations are either linear (type-I) or quadratic (type-II). We give a general framework to interpolate between relativistic and non-relativistic NG modes, revealing a nature of type-I and II NG modes in non-relativistic theories. The interpolating Lagrangians have the nonlinear Lorentz invariance which reduces to the Galilei or Schrodinger invariance in the non-relativistic limit. We find that type-I and type-II NG modes in the interpolating region are accompanied with a Higgs mode and a chiral NG partner, respectively, both of which are gapful. In the ultra-relativistic limit, a set of a type-I NG mode and its Higgs partner remains, while a set of type-II NG mode and gapful NG partner turns to a set of two type-I NG modes. In the non-relativistic limit, the both types of accompanied gapful modes become infinitely massive, disappearing from the spectrum. The examples contain a phonon in Bose-Einstein condensates, a magnon in ferromagnets, and a Kelvon and dilaton-magnon localized around a skyrmion line in ferromagnets.Comment: 20 pages, no figur

Kelvin modes as Nambu-Goldstone modes along superfluid vortices and relativistic strings: finite volume size effects

We study Kelvin modes and translational zero modes excited along a quantized vortex and relativistic global string in superfluids and a relativistic field theory, respectively, by constructing the low-energy effective theory of these modes. We find that they become exact gapless Nambu-Goldstone modes only in a system with infinite volume limit. On the other hand, in a system with the finite volume, we find an imaginary massive gap causing the tachyonic instability above some critical wavelength in the relativistic theory. We also find in the non-relativistic theory that Kelvin modes with wavelengths longer than some critical value propagate in the direction opposite to those with shorter length, contrary to conventional understanding. The number of Nambu-Goldstone modes also saturate the equality of the Nielsen-Chadha inequality for both relativistic and non-relativistic theories.Comment: 9 pages, v2: published versio

Localization of Bose-Einstein Condensation and Disappearance of Superfluidity of Strongly Correlated Bose Fluid in a Confined Potential

We develop a Bose fluid model in a confined potential to consider the new quantum phase due to the localization of Bose-Einstein condensation and disappearance of superfluidity which is recently observed in liquid 4He in porous glass at high pressures. A critical pressure of the transition to this phase can be defined by our new analytical criterion of supposing the size of localized Bose-Einstein condensate becomes comparable to the scale of confinement. The critical pressure is quantitatively consistent with observations without free parameters.Comment: 2 pages, 1 figur

Torus knots as Hopfions

We present a direct connection between torus knots and Hopfions by finding stable and static solutions of the extended Faddeev-Skyrme model with a ferromagnetic potential term. (P,Q)--torus knots consisting of |Q| sine-Gordon kink strings twisted P/Q times into the poloidal cycle along the toroidal cycle on a toroidal domain wall carry the Hopf charge PQ, which demonstrates that Hopfions can be further classified according to torus knot type.Comment: 6 pages, 4 figures, v2: published versio