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Michikazu Kobayashi

Publications and source records attributed to Michikazu Kobayashi.

At least 19 recordsLinked to original sources
arXiv2026

Non-Abelian Quantum Turbulence in Spinor Bose-Einstein Condensates

We numerically investigate statistically steady quantum turbulence in the cyclic phase of a spin-2 spinor Bose--Einstein condensate (BEC) driven by large-scale energy injection via a divergence-free external velocity field. In the full non-Abelian cyclic system, the mass-current spectrum exhibits an anomalous $k^{-7/3}$ scaling, whereas the spin-current spectrum approximately follows a $k^{-5/3}$ power law. To isolate the role of non-Abelian vortex dynamics, we compare this system with an Abelian-restricted cyclic system sharing the same Hamiltonian parameters and driving conditions. Strikingly, the Abelian restriction collapses both the mass- and spin-current spectra into a $k^{-5/3}$ scaling, identical to that of a scalar BEC, despite the three distinct turbulent states maintaining nearly identical vortex-line densities. A Helmholtz decomposition reveals that the mass- and spin-current spectra are predominantly incompressible and transverse, respectively, thereby confirming that the anomalous scaling cannot be attributed simply to compressible fluctuations or to the transverse nature of the energy injection. Local spectral exponents further quantify these distinct scaling regimes. The disappearance of the mass-spin spectral separation under the Abelian restriction, alongside the formation of a large-scale web of rung-connected non-Abelian vortices, provides compelling evidence that non-Abelian vortex dynamics fundamentally govern the organization of turbulent mass flow.

cond-mat.quant-gas↗
arXiv2026

BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional $U(1)$ Ginzburg--Landau Model

We study a one-dimensional fractional $U(1)$ Ginzburg--Landau model whose quadratic part has Fourier multiplier $|k|^σ$, focusing on the marginal case $σ=1$. This dispersion yields logarithmic spin-wave fluctuations, suggesting BKT-like behavior despite the one-dimensional setting. We sample the equilibrium Gibbs measure using stochastic Gross--Pitaevskii dynamics and analyze correlation functions, dimensionless ratios, effective exponents, and twist responses. The correlation function shows a low-temperature algebraic branch with a temperature-dependent exponent, while the high-temperature regime exhibits a nonlocal-kernel-induced tail consistent with $C(r)\sim r^{-2}$. The correlation and Binder ratios are nearly size independent at low temperature and collapse with the BKT-type variable $(T-T_{\rm BKT})(\log L)^2$; finite-size effects set in around $T\simeq0.35\text{--}0.4$, consistent with $T_{\rm BKT}\simeq0.35$. Unlike the two-dimensional XY model, twist responses do not yield a finite helicity modulus: the ordinary linear-response quantity grows with system size, whereas the cusp twist response scales as $L^{-η(T)}$, like the squared zero-mode order parameter. Thus, the transition is BKT-like in correlation scaling, but lacks a universal helicity-modulus jump.

cond-mat.stat-mech↗
arXiv2026

Violation of local equilibrium thermodynamics in one-dimensional Hamiltonian-Potts model

We investigate nonequilibrium phase coexistence associated with a first-order phase transition by numerically studying a one-dimensional Hamiltonian-Potts model with fractional spatial derivatives. The fractional derivative is introduced so as to reproduce the low-wave-number density of states of the standard two-dimensional model, allowing phase coexistence to occur in a minimal one-dimensional setting under steady heat conduction. By imposing a constant heat flux through boundary heat baths, we observe the stable coexistence of ordered and disordered phases separated by a stationary interface. We find that the temperature at the interface systematically deviates from the equilibrium transition temperature, demonstrating a clear violation of the local equilibrium description. This deviation indicates that equilibrium metastable states can be stabilized and controlled by a steady heat current. Furthermore, the interface temperature obtained in our simulations is in quantitative agreement with the prediction of global thermodynamics for nonequilibrium steady states. These results confirm that the breakdown of local equilibrium and the stabilization of metastable states are intrinsic features of nonequilibrium first-order phase transitions, independent of spatial dimensionality. Our study thus provides a minimal and controlled numerical model for exploring the fundamental limits of thermodynamic descriptions in nonequilibrium steady states.

cond-mat.stat-mech↗
arXiv2024

Quantum Knots that Never Come Untied

Lord Kelvin proposed that atoms form hydrodynamic vortex knots. However, they typically untie through reconnections, i. e., local cut-and-slice events, unlike stable vortex unknots such as smoke rings. The same holds in superfluids--quantum fluids with zero viscosity--where vortices have quantized circulation, making them topologically stable. For over 150 years, hydrodynamically stable vortex knots have been sought both experimentally and theoretically. Here, we present the first demonstration of hydrodynamically stable vortex knots and links in experimentally realizable Bose-Einstein condensates of ultracold atomic gases and confirm it through dynamic simulations. Our method creates stable knotted vortex structures in systems where reconnections are prohibited, with potential relevance to neutron star interiors. Additionally, we anticipate our mathematical framework could have applications in quantum computation, quantum turbulence, and DNA dynamics, particularly where reconnections are restricted.

cond-mat.quant-gas↗
arXiv2023

Phase transition in urban agglomeration and segregation

A model of the urban agglomeration and segregation is formulated, in which two types of agents move around on the square-lattice aligned cells. The model is shown to exhibit, when the density of agents are varied as the control parameter, various phase transitions representing appearance of urban aggregation, segregation and social disorder.

physics.soc-ph↗
arXiv2023

Control of Metastable States by Heat Flux in the Hamiltonian Potts Model

The local equilibrium thermodynamics is a basic assumption of macroscopic descriptions of the out of equilibrium dynamics for Hamiltonian systems. We numerically analyze the Hamiltonian Potts model in two dimensions to study the violation of the assumption for phase coexistence in heat conduction. We observe that the temperature of the interface between ordered and disordered states deviates from the equilibrium transition temperature, indicating that metastable states at equilibrium are stabilized by the influence of a heat flux. We also find that the deviation is described by the formula proposed in an extended framework of the thermodynamics.

cond-mat.stat-mech↗
arXiv2023

Proximity effects of vortices in neutron $^3P_2$ superfluids in neutron stars: Vortex core transitions and covalent bonding of vortex molecules

Neutron $^3P_2$ superfluids consisting of neutron pairs with the total angular momentum $J=2$ with spin-triplet and $P$-wave are believed to be realized in neutron star cores. Within the Ginzburg-Landau theory it was previously found that a singly quantized vortex is split into two half-quantized non-Abelian vortices connected by one (or three) soliton(s) forming a vortex molecule with the soliton bond(s), in the absence (presence) of magnetic field parallel to them. In this paper, we investigate proximity effects of two vortex molecules by exhausting all possible two vortex molecule states consisting of four half-quantized vortices and determining the phase diagram spanned by the magnetic field and rotation speed. As the rotation speed is increased, the distance between the two vortex molecules becomes shorter. In the magnetic field below the critical value, we find that as the rotation speed is increased, the two separated vortex molecules transit to a dimerized vortex molecule, where the two vortex molecules are bridged by two solitons that we call "covalent bonds" in analogy with chemical molecules. We also find that the orders of the constituent half-quantized vortex cores transit from a ferromagnetic order to a cyclic order as the vortex molecules come closer. On the other hand, no dimerization occurs in the magnetic field above the critical value. Instead, we find a transition for the polarization direction of the vortex molecules from a configuration parallel to the separation to one perpendicular to the separation as they come closer. We also show some examples of three and four vortex molecule states.

nucl-th↗
arXiv2022

Core structures of vortices in Ginzburg-Landau theory for neutron $^3P_2$ superfluids

We investigate vortex solutions in the Ginzburg-Landau theory for neutron $^3P_2$ superfluids relevant for neutron star cores in which neutron pairs possess the total angular momentum $J=2$ with spin-triplet and $P$ wave, in the presence of the magnetic field parallel to the angular momentum of vortices. The ground state is known to be in the uniaxial nematic (UN) phase in the absence of magnetic field, while it is in the $D_2$ ($D_4$) biaxial nematic (BN) phase in the presence of the magnetic field below (above) the critical value. We find that a singly quantized vortex always splits into two half-quantized non-Abelian vortices connected by soliton(s) as a vortex molecule with any strength of the magnetic field. In the UN phase, two half-quantized vortices with ferromagnetic cores are connected by a linear soliton with the $D_4$ BN order. In the $D_2$ ($D_4$) BN phase, two half-quantized vortices with cyclic cores are connected by three linear solitons with the $D_4$ ($D_2$) BN order. The energy of the vortex molecule monotonically increases and the distance between the two half-quantized vortices decreases with the magnetic field increases, except for a discontinuously increasing jump of the distance at the critical magnetic field. We also construct an isolated half-quantized non-Abelian vortex in the $D_4$ BN phase.

nucl-th↗
arXiv2020

Quantum turbulence simulations using the Gross-Pitaevskii equation: high-performance computing and new numerical benchmarks

This paper is concerned with the numerical investigation of Quantum Turbulence (QT) described by the Gross-Pitaevskii (GP) equation. Numerical simulations are performed using a parallel (MPI-OpenMP) code based on a pseudo-spectral spatial discretization and second order splitting for the time integration. We start by revisiting (in the framework of high-performance/high-accuracy computations) well-known GP-QT settings, based on the analogy with classical vortical flows: Taylor-Green (TG) vortices and Arnold-Beltrami-Childress (ABC) flow. Two new settings are suggested to build the initial condition for the QT simulation. They are based on the direct manipulation of the wave function by generating a smoothed random phase (SRP) field, or seeding random vortex rings (RVR) pairs. The new initial conditions have the advantage to be simpler to implement than the TG and ABC approaches, while generating statistically equivalent QT fields. Each of these four GP-QT settings is described in detail by defining corresponding benchmarks that could be used to validate/calibrate new GP codes. We offer a comprehensive description of the numerical and physical parameters of each benchmark. We analyze the results in detail and present values, spectra and structure functions of main quantities of interest (energy, helicity, etc.) that are useful to describe the turbulent flow. Some general features of QT are identified, despite the variety of initial states.

physics.flu-dyn↗
arXiv2020

Vortex confinement transitions in the modified Goldstone model

The modified XY model is a variation of the XY model extended by a half periodic term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of the modified XY model. We construct a vortex, a soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of this model. Then we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only at one but at two end points in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected.

cond-mat.stat-mech↗
arXiv2019

$\mathbb{Z}_n$ modified XY and Goldstone models and vortex confinement transition

The modified XY model is a modification of the XY model by addition of a half-periodic term. The modified Goldstone model is a regular and continuum version of the modified XY model. The former admits a vortex molecule, that is, two half-quantized vortices connected by a domain wall, as a regular topological soliton solution to the equation of motion while the latter admits it as a singular configuration. Here we define the ${\mathbb Z}_n$ modified XY and Goldstone models as the $n=2$ case to be the modified XY and Goldstone models, respectively. We exhaust all stable and metastalble vortex solutions for $n=2,3$ and find a vortex confinement transition from an integer vortex to a vortex molecule of $n$ $1/n$-quantized vortices, depending on the ratio between the term of the XY model and the modified term. We find for the case of $n=3$, a rod-shaped molecule is the most stable while a Y-shaped molecule is metastable. We also construct some solutions for the case of $n=4$.The vortex confinement transition can be understood in terms of the ${\mathbb C}/{\mathbb Z}_n$ orbifold geometry.

hep-th↗
arXiv2019

Berezinskii-Kosterlitz-Thouless transition of two-component Bose mixtures with inter-component Josephson coupling

We study the Berezinskii-Kosterlitz-Thouless (BKT) transition of two-component Bose mixtures in two spatial dimensions. When phases of both components are decoupled, half-quantized vortex-antivortex pairs of each component induce two-step BKT transitions. On the other hand, when phases of the both components are synchronized through the inter-component Josephson coupling, two species of vortices of each component are bind to form a molecule, and in this case, we find that there is only one BKT transition by molecule-antimolecule pairs. Our results can be tested by two weakly-connected Bose systems such as two-component ultracold dilute Bose mixtures with the Rabi oscillation, and multiband superconductors.

cond-mat.stat-mech↗
arXiv2019

Berezinskii-Kosterlitz-Thouless transition of spin-1 spinor Bose gases in the presence of the quadratic Zeeman effect

We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group $\mathbb{Z}$, and $\mathbb{Z}_2$ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.

cond-mat.quant-gas↗
arXiv2019

Reexamining Ginzburg-Landau theory for neutron $^3P_2$ superfluidity in neutron stars

The Ginzburg-Landau (GL) effective theory is a useful tool to study a superconductivity or superfluidity near the critical temperature, and usually the expansion up to the 4th order in terms of order parameters is sufficient for the description of the second-order phase transition. In this paper, we discuss the GL equation for the neutron $^{3}P_{2}$ superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the 8th order in the condensates and find that this order is necessary for the system to have the unique ground state, unlike the ordinary cases. Starting from the $LS$ potential, which provides the dominant attraction between two neutrons at the high density, we derive the GL equation in the path-integral formalism, where the auxiliary field method and the Nambu-Gor'kov representation are used. We present the detailed description for the trace calculation necessary in the derivation of the GL equation. As numerical results, we show the phase diagram of the neutron $^{3}P_{2}$ superfluidity on the plane spanned by the temperature and magnetic field, and find that the 8th order terms lead to a first-order phase transition, whose existence was predicted in the Bogoliubov-de Gennes equation but has not been found thus far within the framework of the GL expansion up to the 6th order.The first-order phase transition will affect the interior structures inside the neutron stars.

nucl-th↗
arXiv2018

Is a doubly quantized vortex dynamically unstable in uniform superfluids?

We revisit the fundamental problem of the splitting instability of a doubly quantized vortex in uniform single-component superfluids at zero temperature. We analyze the system-size dependence of the excitation frequency of a doubly quantized vortex through large-scale simulations of the Bogoliubov--de Gennes equation, and find that the system remains dynamically unstable even in the infinite-system-size limit. Perturbation and semi-classical theories reveal that the splitting instability radiates a damped oscillatory phonon as an opposite counterpart of a quasi-normal mode.

cond-mat.quant-gas↗
arXiv2016

Universal Critical Behavior at a Phase Transition to Quantum Turbulence

Turbulence is one of the most prototypical phenomena of systems driven out of equilibrium. While turbulence has been studied mainly with classical fluids like water, considerable attention is now drawn to quantum turbulence (QT), observed in quantum fluids such as superfluid helium and Bose-Einstein condensates. A distinct feature of QT is that it consists of quantum vortices, by which turbulent circulation is quantized. Yet, under strong forcing, characteristic properties of developed classical turbulence such as Kolmogorov's law have also been identified in QT. Here, we study the opposite limit of weak forcing, i.e., the onset of QT, numerically, and find another set of universal scaling laws known for classical non-equilibrium systems. Specifically, we show that the transition belongs to the directed percolation universality class, known to arise generically in transitions into an absorbing state, including transitions to classical shear-flow turbulence after very recent studies. We argue that quantum vortices play an important role in our finding.

cond-mat.quant-gas↗
arXiv2016

Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle

We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II su- perconductors, magnetic materials and aspects of cosmology. We characterise the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully-packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls-off algebraically and we associate it to a geometric percolation transition that we characterise in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermo- dynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach towards a state that, within numerical accuracy, shares many features with the one at the percolation threshold, a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops, and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length-scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.

cond-mat.supr-con↗