arXiv subjects

Michikazu Kobayashi

Publications and source records attributed to Michikazu Kobayashi.

At least 37 records · Page 2Linked to original sources

arXiv2016

Dynamics of trapped interacting vortices in Bose-Einstein condensates: Role of breathing degree of freedom

With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose-Einstein condensates in 2 dimensions under the strong repulsive cubic nonlinearity. As for the trial function, we choose a product of two vortex functions assuming a pair interaction and employ the amplitude form of each vortex function in the Padé approximation which accommodates a hallmark of the vortex core. We have obtained Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of Gross-Pitaevskii equation. In higher-energy states of 2 vortex systems, the breathing width degree of freedom plays role of a kicking in the kicked rotator and generates chaos with a structure of sea-urchin needles. Byproduct of the present variational approach includes: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.

nlin.CD↗

arXiv2016

Thermal quenches in the stochastic Gross-Pitaevskii equation: morphology of the vortex network

We study the evolution of 3d weakly interacting bosons at finite chemical potential with the stochastic Gross-Pitaevskii equation. We fully characterise the vortex network in an out of equilibrium. At high temperature the filament statistics are the ones of fully-packed loop models. The vortex tangle undergoes a geometric percolation transition within the thermodynamically ordered phase. After infinitely fast quenches across the thermodynamic critical point deep into the ordered phase, we identify a first approach towards the critical percolation state, a later coarsening process that does not alter the fractal properties of the long vortex loops, and a final approach to equilibrium. Our results are also relevant to the statistics of linear defects in type II superconductors, magnetic materials and cosmological models.

cond-mat.stat-mech↗

arXiv2015

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.

hep-th↗

arXiv2015

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

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.

cond-mat.other↗

arXiv2014

Non-relativistic Nambu-Goldstone modes associated with spontaneously broken space-time and internal symmetries

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 non-relativistic 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) sigma model, a magnetic domain wall in ferromagnets with an easy axis.

hep-th↗

arXiv2014

Non-relativistic Nambu-Goldstone modes propagating along a skyrmion line

We study Nambu-Goldstone (NG) modes or gapless modes propagating along a skyrmion (lump) line in a relativistic and non-relativistic O(3) sigma model, the latter of which describes isotropic Heisenberg ferromagnets. We show for the non-relativistic 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.

hep-th↗

arXiv2014

Color Magnetism in Non-Abelian Vortex Matter

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 $CP^{N-1}$ nonlinear sigma model with spatially anisotropic couplings. We identify gapless excitations independent from Tkachenko modes as color magnons, that is, Nambu-Goldstone modes propagating in the vortex lattice with an anisotropic linear dispersion relation $ω_p^2 = c_{xy}^2(p_x^2+p_y^2) + c_z^2 p_z^2$. We calculate the transition temperature between the ordered and disordered phases, and apply it to dense quark matter. We also identify the order parameter spaces for color anti-ferromagnets.

hep-ph↗

arXiv2014

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.

hep-th↗

arXiv2013

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.

hep-th↗

arXiv2013

Vortex polygons and their stabilities in Bose-Einstein condensates and field theory

We study vortex polygons and their stabilities in miscible two-component Bose-Einstein condensates, and find that vortex polygons are stable for the total circulation $Q \leq 5$, metastable for $Q = 6$, and unstable for $Q \geq 7$. As a related model in high-energy physics, we also study the vortex polygon of the baby-Skyrme model with an anti-ferromagnetic potential term, and compare both results.

cond-mat.quant-gas↗

arXiv2013

Fractional vortex molecules and vortex polygons in a baby Skyrme model

We construct a molecule of fractional vortices with fractional topological lump charges as a baby Skyrmion with the unit topological lump charge in the anti-ferromagnetic (or XY) baby Skyrme model, that is, an O(3) sigma model with a four derivative term and an anti-ferromagnetic or XY-type potential term quadratic in fields. We further construct configurations with topological lump charges Q <= 7 and find that bound states of vortex molecules constitute regular polygons with 2Q vertices as vortices, where the rotational symmetry SO(2) in real space is spontaneously broken into a discrete subgroup Z_Q. We also find metastable and arrayed bound states of fractional vortices for Q=5,6. On the other hand, we find for Q=7 that the regular polygon is metastable and the arrayed bound state is stable. We calculate binding energies of all configurations.

hep-th↗

arXiv2013

Winding Hopfions on R^2 x S^1

We study Hopfions in the Faddeev-Skyrme model with potential terms on R^2 x S^1. Apart from the conventional Hopfions, there exist winding Hopfions, that is, the lump (baby Skyrmion) strings with the lump charge Q with the U(1) modulus twisted P times along S^1, having the Hopf charge PQ. We consider two kinds of potential terms, that is, the potential linear in the field and the ferromagnetic potential with two easy axes, and present stable solutions numerically. We also point out that a Q-lump carries the unit Hopf charge per the period in d=2+1.

hep-th↗

arXiv2013

Jewels on a wall ring

We construct a stable domain wall ring with lump beads on it in a baby Skyrme model with a potential consisting of two terms linear and quadratic in fields.

hep-th↗

arXiv2013

Toroidal domain walls as Hopfions

We construct stable domain walls in a shape of a torus in the Faddeev-Skyrme model with a quadratic potential term admitting two discrete vacua. The phase modulus of the domain wall is twisted P and Q times along the toroidal and poloidal cycles of the torus, respectively, where Q represents the constituent lump charge. We find that these solutions carry the Hopf charge PQ and can be regarded as Hopfions. The toroidal domain walls are characterized by the two topological charges (P,Q), unlike the conventional Hopfions characterized by only the Hopf charge. We explicitly construct stable solutions of the toroidal domain walls with P, Q = 1,2,3, yielding the Hopf charges 1,2,3,4,6,9.

hep-th↗

arXiv2012

Dynamics of inertial vortices in multi-component Bose-Einstein condensates

With use of the nonlinear Schr{ö}dinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multi-component Bose-Einstein condensates (BECs) with a harmonic trap in 2 dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The inter-particle (vortex-vortex) interaction is singularly-repulsive and short-ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. "Chaos in the three-body problem" in the three vortices system can be seen, which is not expected in the corresponding point vortices without inertia in 2 dimensions.

cond-mat.quant-gas↗

arXiv2012

Quantum hydrodynamics

Quantum hydrodynamics in superfluid helium and atomic Bose-Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function appears because of Bose-Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in 4He, which has no analogue with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), "Quantized vortices in superfluid helium and atomic Bose--Einstein condensates", and other review articles.

cond-mat.other↗

arXiv2011

Abe homotopy classification of topological excitations under the topological influence of vortices

Topological excitations are usually classified by the $n$th homotopy group $π_n$. However, for topological excitations that coexist with vortices, there are case in which an element of $π_n$ cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of $π_n$ corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of $π_1$ on $π_n$. In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group $κ_n$. The $n$th Abe homotopy group $κ_n$ is defined as a semi-direct product of $π_1$ and $π_n$. In this framework, the action of $π_1$ on $π_n$ is understood as originating from noncommutativity between $π_1$ and $π_n$. We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is $S^n/K$, where $S^n$ is an $n$-dimensional sphere and $K$ is a discrete subgroup of $SO(n+1)$. We show that the influence of vortices on a topological excitation exists only if $n$ is even and $K$ includes a nontrivial element of $O(n)/SO(n)$.

math-ph↗

arXiv2011

Vortex Tiling in a Spin-2 Spinor Bose-Einstein Condensate

We point out that the internal spin symmetry of the order parameter manifests itself at the core of a fractional vortex in real space without spin-orbit coupling. Such symmetry breaking arises from a topological constraint and the commensurability between spin symmetries of the order parameters inside and outside the core. Our prediction can be applied to probe the cyclic order parameter in a rotating spin-2 $^{87}$Rb condensate as a non-circular vortex core in a biaxial nematic state.

cond-mat.quant-gas↗