Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates

Tsubota, Makoto; Kasamatsu, Kenichi

doi:10.1007/s10909-005-2236-9

Cited by 5 publications

(4 citation statements)

References 72 publications

(123 reference statements)

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“…In laboratory and numerical experiments, it is observed that the vortex tangle is polarized; the average vorticity projected along the rotation axis is not zero (Finne et al 2003;Tsubota et al 2004;Tsubota & Kasamatsu 2005). This is because, under these experimental conditions, one has β 1 > ∼ β 4 v ns /(κΩ 2 ) 1/2 in equation (10), where β 1 is the polarizationinducing term.…”

Section: Glitch: Decay Of the Tanglementioning

confidence: 99%

Transitions between Turbulent and Laminar Superfluid Vorticity States in the Outer Core of a Neutron Star

Peralta

Melatos

Giacobello

et al. 2006

ApJ

107

147

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We investigate the global transition from a turbulent state of superfluid vorticity (quasi-isotropic vortex tangle) to a laminar state (rectilinear vortex array), and vice versa, in the outer core of a neutron star. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations for a rotating superfluid in a differentially rotating spherical shell, we find that the meridional counterflow driven by Ekman pumping exceeds the Donnelly-Glaberson threshold throughout most of the outer core, exciting unstable Kelvin waves which disrupt the rectilinear vortex array, creating a vortex tangle. In the turbulent state, the torque exerted on the crust oscillates, and the crust-core coupling is weaker than in the laminar state. This leads to a new scenario for the rotational glitches observed in radio pulsars: a vortex tangle is sustained in the differentially rotating outer core by the meridional counterflow, a sudden spin-up event (triggered by an unknown process) brings the crust and core into corotation, the vortex tangle relaxes back to a rectilinear vortex array (in < ∼ 10 5 s), then the crust spins down electromagnetically until enough meridional counterflow builds up (after < ∼ 1 yr) to reform a vortex tangle. The turbulent-laminar transition can occur uniformly or in patches; the associated time-scales are estimated from vortex filament theory. We calculate numerically the global structure of the flow with and without an inviscid superfluid component, for Hall-Vinen (laminar) and Gorter-Mellink (turbulent) forms of the mutual friction. We also calculate the post-glitch evolution of the angular velocity of the crust and its time derivative, and compare the results with radio pulse timing data, predicting a correlation between glitch activity and Reynolds number. Terrestrial laboratory experiments are proposed to test some of these ideas.

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Section: Glitch: Decay Of the Tanglementioning

confidence: 99%

Transitions between Turbulent and Laminar Superfluid Vorticity States in the Outer Core of a Neutron Star

Peralta

Melatos

Giacobello

et al. 2006

ApJ

107

147

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“…This must be valid both in classical and superfluid liquids [14]. What is different is the parameter ǫ: it is determined by the dissipation mechanism which is different in two liquids.…”

Section: Kolmogorov Cascadementioning

confidence: 99%

Classical and quantum regimes of superfluid turbulence

Volovik

2003

Jetp Lett.

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We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q −1 playing the same role as the Reynolds number Re = U R/ν in classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re ≫ 1 in classical hydrodynamics, and q ≪ 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is the superfluid Reynolds number Re s = U R/κ, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; and (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. The phase diagram of the dynamical vortex states is suggested.

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“…They are well-known objects, studied in detail theoretically and created in experiments, prior to the work on bright vortex solitons. Results obtained for the "dark vortices", starting from the earliest ones [86][87][88], have been collected in many publications dealing with various settings in photonics [89][90][91][92][93][94][95] (including exciton-polariton condensates [96][97][98], where the vortices exist in dissipative media) and BEC [61,[99][100][101][102][103][104][105], as well as in quantum Fermi gases [106,107]; see also book [108] for an overview of the theme. The studies of vortices in this context are also known as "singular optics", with pivots of the vortices considered as singularities of optical fields; many publications on the latter theme were collected in a special issue of Journal of Optics [109] (see also book [110]).…”

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confidence: 99%

(INVITED) Vortex solitons: Old results and new perspectives

Malomed

2019

Physica D: Nonlinear Phenomena

166

115

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A comparative review is given of some well-known and some recent results obtained in studies of two-and three-dimensional (2D and 3D) solitons, with emphasis on states carrying embedded vorticity. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to instabilities induced by the occurrence of the critical and supercritical collapse, respectively, in the 2D and 3D models with the cubic self-focusing nonlinearity. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review addresses in detail two well-established topics, viz., the stabilization of vortex solitons by means of competing nonlinearities, or by trapping potentials (harmonic-oscillator and spatially-periodic ones). The former topic includes a new addition, closely related to the recent breakthrough, viz., the prediction and creation of robust quantum droplets. Two other topics included in the review outline new schemes which were recently elaborated for the creation of stable vortical solitons in BEC. One scheme relies on the use of the spin-orbit coupling (SOC) in binary condensates with cubic intrinsic attraction, making it possible to predict stable 2D and 3D solitons, which couple or mix components with vorticities S = 0 and ±1 (semi-vortices (SVs) or mixed modes (MMs), respectively). In this system, the situation is drastically different in the 2D and 3D geometries. In 2D, the SOC helps to create a ground state (GS, which does not exist otherwise), represented by stable SV or MM solitons, whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow one to create a GS, but metastable solitons of the SV and MM types can be constructed. Another new scheme makes it possible to create stable 2D vortex-ring solitons with arbitrarily high S in a binary BEC with components coupled by microwave radiation. Some other topics are addressed briefly, such as vortex solitons in dissipative media, and attempts to create vortex solitons in experiments.List of acronyms: 1D -one-dimensional; 2D -two dimensional; 3D -three-dimensional; BEC -Bose-Einstein condensate; CGLE -complex Ginzburg-Landau equation; CQ -cubic-quintic (nonlinearity), FF -fundamental frequency; GPE -Gross-Pitaevskii equation; GS -ground state; GVD -group-velocity dispersion; HO -harmonic oscillator (potential); HV -hidden vorticity; LHY -Lee-Huang-Yang (correction to the mean-field dynamics of BEC); MF -mean field; MM -mixed mode; NLSE -nonlinear Schrödinger equation; OL -optical lattice; PT -parity-time (symmetry); QD -quantum droplet; SH -second harmonic; SOC -spin-orbit coupling; SV -semi-vortex; TF -Thomas-Fermi (approximation); TS -Townes' soliton; VA -variational approximation; VAV -vortex-antivortex (composit...

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Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates

Cited by 5 publications

References 72 publications

Transitions between Turbulent and Laminar Superfluid Vorticity States in the Outer Core of a Neutron Star

Transitions between Turbulent and Laminar Superfluid Vorticity States in the Outer Core of a Neutron Star

Classical and quantum regimes of superfluid turbulence

(INVITED) Vortex solitons: Old results and new perspectives

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