A numerical investigation of vortex-coupled superfluidity

We have performed numerical simulations of quantized vortex lines in a model of normal fluid turbulence. The results are used to discuss the idea, put forward to explain some recent experiments, that in isothermal turbulent helium flow the high density of vortex lines locks the two fluid components together.     

Theory of the effect of heat currents on the velocity of second sound in liquid helium

An explanation of the decrease of the velocity of second sound due to heat currents in liquid helium is given. The explanation is based on Hall and Vinen's theory of the interaction of second sound with vortex lines. The predictions are in reasonable agreement with experiment.     

The escape of positive ions from quantized vortex lines in superfluid helium

We have observed trapping of positive ions by quantized vortex lines in superfluid helium. The thermally activated escape rate has been measured as a function of temperature and electric field and is compared with existing theories and a model calculation.     

Modeling of classical turbulence by quantized vortices

Quantum turbulence in superfluids appears as a stochastic tangle of quantized vortex lines. Interest to this system extends beyond the field of superfluid helium to include a large variety of topics both fundamental and engineering problem. In the article we present a discussion of the hot topic, which is undoubtedly mainstream in this field, and which deals with the quasi-classical properties of quantum turbulence. The idea that classical turbulence can be modeled by a set of slim vortex tubes (or vortex sheets) has been discussed for quite a long time. In classical fluids, the concept of thin vortex tubes is a rather fruitful mathematical model. Quantum fluids, where the vortex filaments are real objects, give an excellent opportunity for the study of the question, whether the dynamics of a set of vortex lines is able to reproduce (at least partially) the properties of real hydrodynamic turbulence. The main goal of this article is to discuss the current state of this activity. We cover such important topics as theoretical justification of this model, and experimental and numerical evidence for quasi-classical turbulence.     

Self-trapping of electrons in vortex rings in liquid helium

A model according to which “fast” and “exotic” negative ions in superfluid helium are the localized states of electrons in vortex rings has been presented. The quantization of radial and longitudinal motions of electrons inside the vortex core and the quantization of the vortex motion of liquid helium lead to the existence of a whole family of excited states of electron vortices, in qualitative agreement with the experiments on the mobility of exotic ions. The possibility of the verification of conclusions of the model in optical experiments has been considered.     

Polarization of superfluid turbulence

We show that normal-fluid eddies in turbulent helium II polarize the tangle of quantized vortex lines present in the flow, thus inducing superfluid vorticity patterns similar to the driving normal-fluid eddies. We also show that the polarization is effective over the entire inertial range. The results help explain the surprising analogies between classical and superfluid turbulence which have been observed recently.     

Transitions from vortex lines to sheets: interplay of topology and dynamics in an anisotropic superfluid

In isotropic macroscopic quantum systems vortex lines can be formed while in anisotropic systems also vortex sheets are possible. Based on measurements of superfluid 3He-A, we present the principles which select between these two competing forms of quantized vorticity: sheets displace lines if the frequency of the external drive exceeds a critical limit. The resulting topologically stable state consists of multiple vortex sheets and has much faster dynamics than the state with vortex lines.     

Quantum turbulence: Theoretical and numerical problems

The term “quantum turbulence” (QT) unifies the wide class of phenomena where the chaotic set of one dimensional quantized vortex filaments (vortex tangles) appear in quantum fluids and greatly influence various physical features. Quantum turbulence displays itself differently depending on the physical situation, and ranges from quasi-classical turbulence in flowing fluids to a near equilibrium set of loops in phase transition. The statistical configurations of the vortex tangles are certainly different in, say, the cases of counterflowing helium and a rotating bulk, but in all the physical situations very similar theoretical and numerical problems arise. Furthermore, quite similar situations appear in other fields of physics, where a chaotic set of one dimensional topological defects, such as cosmic strings, or linear defects in solids, or lines of darkness in nonlinear light fields, appear in the system. There is an interpenetration of ideas and methods between these scientific topics which are far apart in other respects. The main purpose of this review is to bring together some of the most commonly discussed results on quantum turbulence, focusing on analytic and numerical studies. We set out a series of results on the general theory of quantum turbulence which aim to describe the properties of the chaotic vortex configuration, starting from vortex dynamics. In addition we insert a series of particular questions which are important both for the whole theory and for the various applications. We complete the article with a discussion of the hot topic, which is undoubtedly mainstream in this field, and which deals with the quasi-classical properties of quantum turbulence. We discuss this problem from the point of view of the theoretical results stated in the previous sections. We also included section, which is devoted to the experimental and numerical suggestions based on the discussed theoretical models.     

The \overline{\mbox{\sf P}}{\sf ANDA} detector at FAIR

Selected problems of collisional processes in exotic atoms are discussed. The emphasis is on the collisional effects in antiprotonic helium including formation of antiprotonic atoms, collisional quenching of hot and thermalized metastable antiprotonic helium, shift and broadening of E1 and M1 spectral lines.     

Equilibrium shape of rotating helium crystals

We have studied theoretically the effects of rotation on the equilibrium shape of the interface between superfluid and solid helium. Surface structures in the shape of hillocks and ridges appear in the presence of a vortex lattice in the superfluid. These structures are very sensitive to the orientation of the interface boundary with respect to the crystal planes when surface stiffness is very anisotropic, as occurs well below the roughening transition. We predict the appearance of ring shaped facets for fast rotation speeds. These effects should be observable by using optical techniques.     

Filament formation by impurities embedding into superfluid helium

The hydrogen molecules embedded in superfluid helium as a gas jet are shown to form long thin filaments. These filaments survived under a helium transition to anormal phase demonstrating their conjugated entity. The concentration of an impurity in the core of the vortex may be the mechanism of the impurity coalescence providing a cotton-like structure of the condensate obtained by introducing an impurity-containing gas helium jet to He-II. The text was submitted by the authors in English.     

Stark broadening of visible neutral helium lines in a plasma

Side-on observations of the visible spectrum emitted by a helium plasma generated in a wall-stabilized arc are reported. Electron densities range from 0.2 to 1.3 × 10²²m^-3 and electron temperatures vary from 10,000 to 20,000 K. Most of the seventeen measured lines are “isolated” at the conditions of the experiment. Here, “isolated” refers to quantum levels which are non-degenerate even in the presence of perturbing fields. Electron densities derived from the Stark-widths of the isolated lines agree to within 15% of the values determined from Hβ and from the quasi-degenerate He(I) lines at 4471 and 4921 Å. Similar agreement is observed for the static-ion Stark broadening parameters. However, at the conditions of this experiment, the static-ion approximation is not valid near the center of some of the isolated lines. The observation of ion-dynamic effects in neutral isolated lines is reported here for the first time. In the isolated lines, the measured ion-dynamic effects are reasonably consistent with calculations based on an adiabatic “unified” theory for the ion perturbers. A simple parametric expression closely approximates the ion-dynamic contribution to the half-width of isolated lines. Hydrogenic (non-isolated) neutral helium lines exhibit a large discrepancy with theoretical profiles near the line center, where ion-dynamic effects are important.     

Rotating superfluid turbulence

Almost all studies of vortex states in helium II have been concerned with either ordered vortex arrays or disordered vortex tangles. This work numerically studies what happens in the presence of both rotation (which induces order) and thermal counterflow (which induces disorder). We find a new statistically steady state in which the vortex tangle is polarized along the rotational axis. Our results are used to interpret an instability that was discovered experimentally by Swanson et al. [Phys. Rev. Lett. 50, 190 (1983)]] and the vortex state beyond the instability that has been unexplained until now.     

Vortex states in mesoscopic superconductors

The results of theoretical investigations of the electronic structure and transport properties of vortex states in mesoscopic superconductors with sizes of several coherence lengths are reviewed. The features of the electronic spectra of multiquantum vortices and vortex molecules, as well as mechanisms of thermal transport along vortex lines, are considered by taking into account boundary effects.     

Absolute measurement of vortex line density in counterflowing hell

The vortex line density in a thermally induced counterflow in helium II is measured by means of attenuation of second sound in a long channel 1 cm × 1 cm in cross section. The line density is calibrated by rotating the channel about its vertical axis. The results are compared with current theories of vortex line turbulence.     

Drag effect and topological complexes in strongly interacting two-component lattice superfluids

The mutual drag in strongly interacting two-component superfluids in optical lattices is discussed. Two competing drag mechanisms are the vacancy-assisted motion and proximity to a quasimolecular state. In a case of strong drag, the lowest energy topological excitation (vortex or persistent current) can consist of several circulation quanta. In the SQUID-type geometry, the circulation can become fractional. We present both the mean field and Monte Carlo results. The drag effects in optical lattices are drastically different from the Galilean-invariant Andreev-Bashkin effect in liquid helium.     

Matrix formulation of hydrodynamics and extension of ptolemaic flows to three-dimensional motions

A new matrix formulation of Lagrange hydrodynamic equations is proposed. Exact solutions of those equations are obtained in matrix form. It is found that precession of vortex lines around some fixed axis in space is a general property of the flows described by those solutions. Two types of fluid motion are studied. Flows of the first type have straight vortex lines, and their particle trajectories are windings on toroidal surfaces. The other flows have plane particle trajectories, and their vortex lines are arbitrarily shaped plane curves. All these motions are shown to be three-dimensional generalizations of plane Ptolemaic flows [1,2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, pp. 783–796, June, 1996.The authors express their gratitude to the Russian Foundation for Fundamental Research for support of these investigations under Grant No. 96-01-00585 and to INTAS Foundation for support under Grant No. 93-1373.     

Reversal of the dipole vortex in a negative index of refraction material

When a small particle is illuminated by a circularly polarized laser beam, the induced electric dipole moment rotates in a plane. The flow lines of the emitted electromagnetic energy are the field lines of the Poynting vector. When the particle is embedded in a dielectric, these field lines have a vortex structure, and the rotation in the vortex has the same orientation as the rotation direction of the dipole. We show that when the embedding medium is a negative index of refraction material, the direction of rotation in the vortex is reversed.     

Manipulating transmission and reflection properties of a photonic crystal doped with quantum dot nanostructures

We consider excitations that exist, in addition to phonons, in the ideal Bose gas at zero temperature. These excitations are vortex rings whose energy spectrum is similar to the roton one in liquid helium.     

Mutual friction in the laminar flow of superfluid helium II through capillary tubes

The Hall-Vinen-Bekarevich-Khalatnikov theory is applied to the laminar flow of superfluid helium through capillary tubes. Velocity profiles obtained for the superfluid are interpreted in terms of the motion of vortex rings. The thermodynamic potential gradient as a function of the average superfluid and normal fluid velocities compares favourably with recent experimental results. It is concluded that the vortex rings originate at the wall and disappear at the tube axis.