Presented is a prediction, based on the Frenet-Serret differential geometry of space curves, that the wave number dependence of the average kinetic energy per unit length of two mutually interacting highly curved quantum vortex scales as k^-3. The interacting quantum vortices are helical in shape, supporting circularly polarized counter-propagating waves, with arbitrary curvature and torsion. This power-law spectrum agrees with the high-k spectrum found in precise quantum simulations of turbulent superfluidity with tangle of highly curved and excited quantum vortices.
Simulation of a sonic black-hole/white-hole pair in a (2+1)-dimensional Bose-Einstein condensate shows formation of superfluid vortices through dynamical instabilities seeded by initial quantum noise. The instabilities saturate in a quasi-steady state of superfluid turbulence within the supersonic region, from which sound waves are emitted in qualitative resemblance to Hawking radiance. The power spectrum of the radiation from the slowly decaying two-dimensional sonic black hole is strongly non-thermal, however.
Supersaturated superfluid 3He-4He liquid mixture, separating into the 3He-concentrated c-phase and 3He-diluted d-phase, represents a unique possibility for studying macroscopic quantum nucleation and quantum phase-separation kinetics in binary mixtures at low temperatures down to absolute zero. One of possible heterogeneous mechanisms for the phase separation of supersaturated d-phase is associated with superfluidity of this phase and with a possible existence of quantized vortices playing a role of nucleation sites for the c-phase of liquid mixture. We analyze the growth dynamics of vortex co…
Critical velocities in superfluids and the nucleation of vortices
超流体的临界速度问题，即对超流体被流动破坏的理解，是一个长期存在的问题。一个困难来自于几种击穿机制的存在。一个主要的进展来自于对单个$2π$相位滑移的观察，这种相位滑移产生于量子化涡旋的成核，即它们的产生{ \it ex nihilo}。的成核过程中的热制度和量子制度的统计特性进行了识别和分析：涡旋成核提供了一个有据可查的情况下，宏观量子隧穿（MQT）。特别是，对超纯$^4$ He获得的实验数据的仔细审查揭示了阻尼对隧道效应的影响，这是一种罕见的情况，可以研究环境对MQT的影响。
One of the most sought-after objects in topological quantum matter systems is a vortex carrying half a quantum of circulation. They were originally predicted to exist in superfluid 3He-A, but have never been resolved there. Here we report an observation of half-quantum vortices (HQVs) in the polar phase of superfluid 3He. The vortices are created with rotation or by the Kibble-Zurek mechanism and identified based on their nuclear magnetic resonance signature. This discovery provides a pathway for studies of unpaired Majorana modes bound to the HQV cores in the polar-distorted A phase.
We perform a numerical simulation of the dynamics of quantized vortices produced by coflow in a square channel using the vortex filament model. Unlike the situation in thermal counterflow, where the superfluid velocity $v_{\rm s}$ and normal-fluid velocity $v_{\rm n}$ flow in opposite directions, in coflow, $v_{\rm s}$ and $v_{\rm n}$ flow in the same direction. Quantum turbulence in thermal counterflow has been long studied theoretically and experimentally, and its various features have been revealed.In recent years, an experiment on quantum turbulence in coflow has been performed to observe …
Peculiar dynamics of a free surface of the superfluid 4He has been observed experimentally with a newly established technique utilizing a number of electrically charged fine metal particles trapped electrically at the surface by Moroshkin et al. They have reported that some portion of the particles exhibit some irregular motions and suggested the existence of quantized vortices interacting with the metal particles. We have conducted calculations with the vortex filament model, which turns out to support the idea of the vortex-particle interactions. The observed anomalous metal particle motions…
We study inelastic interactions of particles with quantized vortices in superfluids by using a semi-classical matter wave theory that is analogous to the Landau two-fluid equations, but allows for the vortex dynamics. The research is motivated by recent experiments on xenon doped helium nanodroplets that show clustering of the impurities along the vortex cores. We numerically simulate the dynamics of trapping and interactions of xenon atoms by quantized vortices in superfluid helium and the obtained results can be extended to scattering of other impurities by quantized vortices. Different ener…
The paper analyzes the transverse forces (the Magnus and the Lorentz forces) on vortices in superfluids put into periodic potentials at $T=0$. The case of weak potential and the tight-binding limit described by the Bose-Hubbard model were addressed. The analysis was based on the balance of true momentum and quasimomentum. A special attention was paid to the superfluid close to the superfluid-insulator transition. In this area of the phase diagram the theory predicts the particle-hole symmetry line where the Magnus force changes sign with respect to that expected from the sign of velocity circu…
In a recent article, Kwon et al. [Nature (London) {\bf 600}, 64 (2021)] revealed nonuniversal dissipative dynamics of quantum vortices in a fermionic superfluid. The enhancement of the dissipative process is pronounced for the Bardeen-Cooper-Schrieffer interaction regime, and it was suggested that the effect is due to the presence of quasiparticles localized inside the vortex core. We test this hypothesis through numerical simulations with time-dependent density-functional theory: a fully microscopic framework with fermionic degrees of freedom. The results of fully microscopic calculations exp…
We show that the Landau vortex-free state in rotating container may give rise to the lattice of spin vortices. We consider this effect on example of spin vortices in magnon Bose-Einstein condensate (the phase coherent spin precession) in the B-phase of superfluid $^3$He, and on example of spin vortices in the polar phase of $^3$He.
Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
研究了由Gross-Pitaevskii方程驱动的量子化超流涡旋中Kelvin波的统计性质。没有人为的强迫或耗散。准确跟踪涡流位置。这一过程直接使我们能够获得凯文波占据数谱。从初始条件下的长时间积分和整体平均获得的数值数据支持[L 'vov和Nazarenko，JETP Lett 91，428（2010）]中提出的谱。惯性范围内的开尔文波模式被发现是高斯弱湍流预测所预期的。最后研究了开尔文波谱的耗散范围。在这个范围内观察到强烈的非高斯波动。
We point out that half-quantized non-Abelian vortices exist as the minimum energy states in rotating neutron $^3P_2$ superfluids in the inner cores of magnetars with magnetic field greater than $3 \times 10^{15}$ Gauss, while they do not in ordinary neutron stars with smaller magnetic fields. One integer vortex is split into two half-quantized vortices. The number of vortices is about $10^{19}$ and they are separated at about $μ$m in a vortex lattice for typical parameters, while the vortex core size is about 10-100 fm. They are non-Abelian vortices characterized by non-Abelian first homotopy …
We study the impact of the non-analytic reconstruction of vortex cores on static vortex structures in weakly coupled superfluids. We show that in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure). Similar instability may be also observable in clean superconducting films.
We present an experimental and theoretical study of the 2D dynamics of electrically charged nanoparticles trapped under a free surface of superfluid helium in a static vertical electric field. We focus on the dynamics of particles driven by the interaction with quantized vortices terminating at the free surface. We identify two types of particle trajectories and the associated vortex structures: vertical linear vortices pinned at the bottom of the container and half-ring vortices travelling along the free surface of the liquid.
Formation of topological defects during symmetry breaking phase transitions via the {\it Kibble mechanism} is extensively used in systems ranging from condensed matter physics to the early stages of the universe. Kibble mechanism uses topological arguments and predicts equal probabilities for the formation of defects and anti-defects. Certain situations, however, require a net bias in the production of defects (or antidefects) during the transition, for example, superfluid transition in a rotating vessel, or flux tubes formation in a superconducting transition in the presence of external magne…
We investigate the coupled dynamics of quantized vortices and normal fluid in superfluid $^4$He at finite temperatures using a numerical approach based on the vortex filament model (VFM) and lattice Boltzmann method (LBM). The LBM allows us to simulate a fluid flow with only local operations, i .e., rather than solving the Navier--Stokes (NS) equations directly; a fluid flow is considered a convection of mesoscopic particles between sites on a lattice grid. Although the two-fluid nature of He II makes its flow complex, the particle-like treatment of the normal fluid in the LBM significantly re…
The polar phase of superfluid $^3$He is stable in "nematically ordered" densed aerogel. A rotating vessel with the polar superfluid can be filled either by an array of the single quantum vortices or by an array of the half-quantum vortices. It is shown that the inhomogeneous distribution of the spin part of the order parameter arising in an array of half-quantum vortices in strong enough magnetic field tilted to the average direction of aerogel strands leads to the appearance of a satellite in the NMR signal shifted in the negative direction with respect to the Larmor frequency. The satellite …
Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid $^3$He, we show that half-quantum vortices (HQVs) -- linear topological defects carrying half quantum of circulation -- survive transitions from the polar phase to other superf…
We have investigated the structure of macroscopic suction flows in superfluid $^4$He. In this study, we primarily analyze the structure of the quantized vortex bundle that appears to play an important role in such systems. Our study is motivated by a series of recent experiments conducted by a research group in Osaka City University [Yano $\textit{et. al.}$, J. Phys. Conf. Ser. $\textbf{969}$, 012002 (2018)]; they created a suction vortex using a rotor in superfluid $^4$He. They also reported that up to $10^4$ quantized vortices accumulated in the central region of the rotating flow. The quant…
