arXiv subjects

Makoto Tsubota

Publications and source records attributed to Makoto Tsubota.

At least 19 recordsLinked to original sources

arXiv2025

Vortex configuration dependent equilibrium and non-equilibrium states in two-dimensional quantum turbulence

In this work, we analyze the evolution of four vortex configurations, namely, dipole, plasma, cluster, and lattice, using the two-dimensional mean-field Gross-Pitaevskii equation, focusing on their dynamical decay and approach to the equilibrium. Our analysis reveals that the cluster vortex configuration reaches equilibrium more rapidly than the others, while the dipole, plasma, and lattice configurations exhibit persistent non-equilibrium behavior, tending toward non-thermal fixed points. Specifically, the cluster configuration follows Kolmogorov-like scaling ($\varepsilon^{i}(k)\sim k^{-5/3}$) in the incompressible spectrum, while the other configurations follow Vinen-like scaling ($\varepsilon^{i}(k)\sim k^{-1}$). In the compressible spectrum, the cluster case exhibits a $k$ scaling, indicating full mode equilibration, while for the other configurations, the modes thermalize only above a critical wave number. Additionally, the transfer function for the cluster configuration displays a Gaussian distribution, typical of equilibrium states, while the other configurations exhibit skewed Gaussian or exponential distributions, indicative of their non-equilibrium nature. Finally, the particle number spectra show that the cluster case follows dynamical scaling closer to equilibrium, while the dipole, plasma, and lattice configurations evolve towards non-thermal fixed points. Our findings provide new insights into the dynamics of vortex configurations and their approach to equilibrium or non-equilibrium states, offering guidance for future studies on quantum turbulence and its control.

cond-mat.quant-gas↗

arXiv2025

Kelvin-Wave-Inspired Optical Vortex Excitation in Kerr Nonlinear Media

We demonstrate a direct one-to-one correspondence between nonlinear optical fields in defocusing Kerr media and wave functions in weakly interacting Bose-Einstein condensates or quantum fluids. Based on this correspondence, we propose the existence of excitations in an optical vortex beam characterized by a helical deformation of its phase singularity core. These excitations are direct analogues of Kelvin waves known in quantum and classical fluid dynamics. We further show that the excitations exhibit two distinct branches, one of which includes a stationary solution. A feasible experimental scheme for generating these excitations is also discussed.

physics.optics↗

arXiv2025

Dissipation and Decay of Three Dimensional Holographic Quantum Turbulence

Quantum turbulence is a far-from-equilibrium process characterized by high nonlinearity. Holographic duality provides a systematic framework for simulating the decaying $(3+1)$-dimensional quantum turbulence by numerically solving the dual Abelian-Higgs theory in a $(4+1)$-dimensional black hole background. We reveal that different types of decay behavior of the total vortex line density $L$ emerge depending on the initial vortex line density, ranging from $L\sim t^{-1.5}$ to $L\sim t^{-1}$, similar to the experimental observation of $^3$He in Phys. Rev. Lett. 96, 035301 (2006), and of $^4$He in Phys. Rev. Lett. 82, 4831 (1999) and in Phys. Rev. Lett. 118, 134501 (2017). Furthermore, by measuring the energy flux at the black hole horizon, we determine that the energy dissipation rate $dE/dt$ is proportional to the square of the total vortex line density, consistent with the vortex line decay equation proposed by W. F. Vinen and also the experimental measurement in Nature Physics 7, 473 - 476 (2011).

hep-th↗

arXiv2025

Quantum Turbulence Across Dimensions: Crossover from two- to three-dimension

We investigate the dynamic transition of quantum turbulence (QT) in a confined potential field as the system evolves from purely two-dimensional (2D) to quasi-two-dimensional, and ultimately to three-dimensional (3D), by fixing the lateral dimensions of the trapping box while varying its height. In the 2DQT, distinct Onsager vortex cluster formation and inverse energy cascade are observed, while 3DQT exhibits a direct energy cascade consistent with the Vinen turbulence decay rate, which display striking differences. By systematically altering the system height, we explore how dimensionality drives the differentiation of turbulence types and find that this transition is closely related to the excitation of Kelvin waves. Kelvin waves not only introduce additional dissipation mechanisms but also serve as mediators for direct energy transfer across scales. When the wavelength of the permitted Kelvin waves exceeds the critical size of vortex clusters, turbulence begins transitioning to 3D type, culminating in fully developed 3DQT at the characteristic scale. In the transitional region, we observe continuous variations in the decay rate and vortex cluster correlation functions.

cond-mat.quant-gas↗

arXiv2025

Universal Turbulent States of Miscible Two-Component Bose-Einstein Condensates

We investigate turbulence in miscible two-component Bose-Einstein condensates confined in a box potential using the coupled Gross-Pitaevskii equations. Turbulence is driven by an oscillating force, causing the components to oscillate either in-phase (co-oscillating) or out-of-phase (counter-oscillating). A parameter measuring component separation (0 for overlap, 1 for full separation) reveals two turbulent states: coupled (the parameter $\sim0$) and decoupled (the parameter $\sim0.5$). Co-oscillating flows transition between these states at a critical interaction strength, while counter-oscillating flows consistently show the decoupled state. A probabilistic model predicts the decoupled state's parameter as $\sqrt{4/π- 1} = 0.523$, consistent with simulations.

cond-mat.quant-gas↗

arXiv2024

Influence of different mutual friction models on two-way coupled quantized vortices and normal fluid in superfluid $^4$He

We study the influence of two mutual friction models on quantized vortices and normal fluid using two-way coupled simulations of superfluid $^4$He. The normal fluid is affected by quantized vortices via mutual friction. A previous study [Y. Tang, et al. Nat. Commun. 14, 2941 (2023)] compared the time evolutions of the vortex ring radius and determined that the self-consistent two-way coupled mutual friction (S2W) model yielded better agreement with the experimental results than the two-way coupled mutual friction (2W) model whose model parameters were determined through experiments with rotating superfluid helium. In this study, we compare the two models in more detail in terms of the quantized vortex ring propagation, reconnection, and thermal counterflow. We show that the S2W model exhibits better results than the 2W model on the microscopic scale near a quantized vortex, such as during quantized vortex ring propagation and reconnection, although the S2W model requires a higher spatial resolution. For complex flows such as a thermal counterflow, the 2W model can be applied even to a low-resolution flow while maintaining the anisotropic normal fluid velocity fluctuations. In contrast, the 2W model predicts lower normal fluid velocity fluctuations than the S2W model. The two models show probability density functions with $- 3$ power-law tails for the normal fluid velocity fluctuations.

cond-mat.other↗

arXiv2024

Corotation of two quantized vortices coupled with collective modes in self-gravitating Bose-Einstein condensates

We numerically examine the corotation of two parallel quantized vortices in a self-gravitating Bose-Einstein condensate (BEC) employing the Gross-Pitaevskii-Poisson equations. The long-range gravitationally attractive interaction allows the BEC to self-confine without the need for external potentials, while the density-dependence of the gravitational potential induces intriguing behaviors in the quantized vortices. The aim of this study is to provide a clue for understanding the corotation of two quantized vortices under the influence of gravitational interactions. The corotation of two quantized vortices is coupled with collective modes of the BEC, which markedly differs from the behavior observed in typical BECs confined by an external potential. The rotational period increases linearly with the initial position from the center of the BEC. This deviation from the quadratic increase observed in a uniform BEC suggests that the gravitational interaction exerts a drag effect on the rotating quantized vortices. The two closely positioned quantized vortices rotate along elliptical orbits with radial fluctuations. However, when the quantized vortices are initially positioned beyond a critical radius comparable to their core sizes, their trajectory transitions into an outward spiral, implying the onset of effective dissipation. Our findings demonstrate that the radial fluctuations of the quantized vortex resonate with the quadrupole mode of the BEC, giving rise to a dissipation mechanism.

cond-mat.other↗

arXiv2024

Macroscopic Efimov effect of quantized vortex

The three-body problem, from the chaotic motions of celestial bodies to complex microscopic particle interactions, has always been one of the most foundational yet intricate challenges in physics since its establishment. A key breakthrough in this domain is the Efimov effect, which represents a significant stride in what is now known as Efimov physics. Our study uncovers a macroscopic Efimov effect in a three-component Bose-Einstein Condensate (BEC) system. Through theoretical analysis and numerical simulation, it is verified that under certain conditions, three vortices form a bound state, while removing one vortex causes the others to unbind, demonstrating topological characteristics similar to the Borromean rings, hence termed the `vortex Efimov effect', signifying a novel topological phase transition. We propose several experimental approaches to realize this macroscopic Efimov effect, paving new paths not only in many-body physics but also in exploring quantum phase transitions and applications in quantum information.

hep-th↗

arXiv2024

Collective Excitations of Self-Gravitating Bose-Einstein Condensates: Breathing Mode and Appearance of Anisotropy under Self-Gravity

We investigate the collective mode of a self-gravitating Bose-Einstein condensate (BEC) described by the Gross-Pitaevskii-Poisson (GPP) equations. The self-gravitating BEC has garnered considerable attention in cosmology and astrophysics, being proposed as a plausible candidate for dark matter. Our inquiry delves into the breathing and anisotropic collective modes by numerically solving the GPP equations and using the variational method. The breathing mode demonstrates a reduction in period with increasing total mass due to the density dependence of the self-gravitating BEC, attributed to the density-dependent nature of self-gravitating BECs, aligning quantitatively with our analytical findings. Additionally, we investigate an anisotropic collective mode in which the quadrupole mode intertwines with the breathing mode. The period of the quadrupole mode exhibits similar total mass dependence to that of the breathing mode. The characteristics of these periods differ from those of a conventional BEC confined by an external potential. Despite the differences in density dependence, the ratio of their periods equals that of the BEC confined by an isotropic harmonic potential. Furthermore, an extension of the variational method to a spheroidal configuration enables the isolation of solely the quadrupole mode from the anisotropic collective mode.

cond-mat.quant-gas↗

arXiv2024

Emergence of isotropy in rotating turbulence of Bose-Einstein condensates

We present a study on the development of rotating turbulence in Bose-Einstein condensates with a dissipative Gross-Pitaevskii model. Turbulence is generated by driving the lattice of quantized vortices in a harmonic potential with a random forcing potential. As the turbulence progressed, the initial alignment of vortices underwent slight disruptions, thereby increasing the high-wavenumber components of the kinetic energy. In the turbulent state, the distribution of incompressible kinetic energy exhibits milder anisotropy than that in the initial lattice state and demonstrates a scaling behavior of $k_z^{-2.5}$ in the direction parallel to the rotation axis. In contrast, the compressible kinetic energy exhibits an isotropic scaling behavior at high wavenumbers.

cond-mat.quant-gas↗

arXiv2024

Emergence of Large-Scale Structures in Holographic Superfluid Turbulence

In two-dimensional turbulence systems, the emergence of large-scale structures holds profound physical implications, particularly as it indicates the occurrence of inverse energy cascades, thereby garnering significant attention. In this paper, we report a novel vortex clusters formation in the background of near-extreme Reissner-Nordstr$\ddot{o}$m black hole holographic model. At temperatures nearing absolute zero, we observe not only the formation of vortex clusters but also the emergence of an inverse energy cascade. Distinct from typical quantum systems, the genesis of holographic vortex clusters is rooted in unique quantum dissipation properties, characterized by the near immobilization of vortex dipoles at low temperatures. Through a comparative analysis with the dynamics of the Gross-Pitaevskii equation, our investigation enhances the understanding of inverse energy cascades under these extreme conditions, thereby broadening our comprehension of quantum turbulence.

hep-th↗

arXiv2024

Direct excitation of Kelvin waves on quantized vortices

Helices and spirals, prevalent across various systems, play a crucial role in characterizing symmetry, describing dynamics, and imparting unique functionalities, attributed to their inherent simplicity and chiral nature. A helical excitation on a quantized vortex, an example of a one-dimensional topological defect, emerges as a Nambu-Goldstone mode following spontaneous symmetry breaking, known as a Kelvin wave. Kelvin waves play a vital role in energy dissipation within inviscid quantum fluids. However, deliberately exciting Kelvin waves has proven to be challenging. Here, we introduce a controlled method for exciting Kelvin waves on a quantized vortex in superfluid helium-4. We used a charged nanoparticle, oscillated by a time-varying electric field, to stimulate Kelvin waves on the vortex. A major breakthrough in our research is the confirmation of the helical nature of Kelvin waves through three-dimensional image reconstruction, providing visual evidence of their complex dynamics. Additionally, we determined the dispersion relation and the phase velocity of the Kelvin wave and identified the vorticity direction, enhancing our understanding of quantum fluid behavior. This work elucidates the dynamics of Kelvin waves and pioneers a novel approach for manipulating and observing quantized vortices in three dimensions, thereby opening new avenues for exploring quantum fluidic systems.

cond-mat.quant-gas↗

arXiv2024

Spontaneous Symmetry Breaking of Vortex Number in Binary Alternating Current Countersuperflow

In binary superfluid counterflow systems, vortex nucleation arises as a consequence of hydrodynamic instabilities when the coupling coefficient and counterflow velocity exceed the critical value. When dealing with two identical components, one might naturally anticipate that the number of vortices generated would remain equal. However, through the numerical experiments of the holographic model and the Gross-Pitaevskii equation, our investigation has unveiled a remarkable phenomenon: in Alternating Current counterflow systems, once the coupling coefficient and frequency exceed certain critical values, a surprising symmetry-breaking phenomenon occurs. This results in an asymmetry in the number of vortices in the two components. We establish that this phenomenon represents a novel continuous phase transition, which, as indicated by the phase diagram, is exclusively observable in Alternating Current counterflow. We provide an explanation for this intriguing phenomenon through soliton structures, thereby uncovering the complex and unique characteristics of quantum fluid instabilities and their rich phenomena.

cond-mat.quant-gas↗

arXiv2023

Universal defect density scaling in an oscillating dynamic phase transition

Universal scaling laws govern the density of topological defects generated while crossing an equilibrium continuous phase transition. The Kibble-Zurek mechanism (KZM) predicts the dependence on the quench time for slow quenches. By contrast, for fast quenches, the defect density scales universally with the amplitude of the quench. We show that universal scaling laws apply to dynamic phase transitions driven by an oscillating external field. The difference in the energy response of the system to a periodic potential field leads to energy absorption, spontaneous breaking of symmetry, and its restoration. We verify the associated universal scaling laws, providing evidence that the critical behavior of non-equilibrium phase transitions can be described by time-average critical exponents combined with the KZM. Our results demonstrate that the universality of critical dynamics extends beyond equilibrium criticality, facilitating the understanding of complex non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2023

Dynamics of pinned quantized vortices in superfluid $^4$He in a microelectromechanical oscillator

We numerically studied the vortex dynamics at zero temperature in superfluid $^4$He confined between two parallel rough solid boundaries, one of which oscillates in a shear mode. This study was motivated by the experimental work by Barquist $et$ $al.$ which employed a microelectromechanical systems (MEMS) oscillator operating in superfluid $^4$He at a near-zero temperature. Their experiments suggest that the motion of the MEMS oscillator is damped by quantized vortices. In our study, we postulated that this damping effect was closely associated with vortex pinning phenomena and developed pinning models. Our primary objective is to understand the vortex dynamics in the presence of pinning and to provide insight into the experimental observations regarding the damping mechanism. We confirmed that Kelvin waves were excited in the pinned vortices when the oscillation frequency of the solid boundary matched with the mode frequency of the Kelvin wave. Additionally, we examined the formation and evolution of vortex tangles between the boundaries. The vortex tangle was suppressed in the presence of pinning, while the absence of pinning allowed to form well developed vortex tangle resulting in turbulence. Finally, by evaluating the tension of pinned vortices we extracted the damping force acting on the solid boundaries.

cond-mat.other↗

arXiv2023

Faraday Waves in Bose-Einstein Condensates -- The Excitation by the Modulation of the Interaction and the Potential

We numerically study the dynamics of Faraday waves for Bose-Einstein condensates(BECs) trapped by anisotropic potentials using the three-dimensional Gross-Pitaevskii equation. In previous studies, Faraday waves were excited by periodic modulation of the interaction or potential; in contrast, this study systematically addresses the excitations of the two methods. When the interaction is modulated with a modulation frequency resonant with Faraday waves, the breathing mode along the tight confinement direction is excited, and the Faraday waves appear in the direction of weak confinement. A modulation frequency that is not resonant with Faraday waves does not excite Faraday waves. Thus, the dynamics depend on modulation frequencies. The behavior of the total energy and its decomposition characterize the dynamics. The excitation of Faraday waves depends on the anisotropy of the potentials as well; Faraday waves are excited only for elongated BECs. We compare the differences of the dynamics in modulation methods. There are no qualitative differences between the modulation of the interaction and potential. When the interaction and potential are simultaneously modulated, Faraday waves are excited but they do not necessarily work additively. To understand this phenomenon as a dynamical system, we choose a few dynamical variables and follow their trajectory in a phase space. The trajectory characteristics of Faraday waves and the breathing mode show that the methods of modulation are not very relevant; determining the target mode to excite is important.

cond-mat.quant-gas↗

arXiv2023

Studies on quantum turbulence with Vinen

In my research career in the field of quantum turbulence, I have been encouraged by Vinen. In this article, I review my works motivated by him and my joint collaborations with him. Vinen encouraged me in studies on quantum turbulence at zero temperature, Kolmogorov spectrum of a vortex tangle without mutual friction, and fully coupled dynamics of quantized vortices and normal fluid. Joint works include studies on diffusion of a vortex tangle, Kelvin wave cascade, quantum turbulence created by an oscillating object, and coupled dynamics of tracer particles and quantized vortices.

cond-mat.other↗

arXiv2023

Emergent isotropy of a wave-turbulent cascade in the Gross-Pitaevskii model

The restoration of symmetries is one of the most fascinating properties of turbulence. We report a study of the emergence of isotropy in the Gross-Pitaevskii model with anisotropic forcing. Inspired by recent experiments, we study the dynamics of a Bose-Einstein condensate in a cylindrical box driven along the symmetry axis of the trap by a spatially uniform force. We introduce a measure of anisotropy $A(k,t)$ defined on the momentum distributions $n(\boldsymbol{k},t)$, and study the evolution of $A(k,t)$ and $n(\boldsymbol{k},t)$ as turbulence proceeds. As the system reaches a steady state, the anisotropy, large at low momenta because of the large-scale forcing, is greatly reduced at high momenta. While $n(\boldsymbol{k},t)$ exhibits a self-similar cascade front propagation, $A(k,t)$ decreases without such self-similar dynamics. Finally, our numerical calculations show that the isotropy of the steady state is robust with respect to the amplitude of the drive.

cond-mat.quant-gas↗