Liquid 4He: Contributions to First Principles Theory. I. Quantized Vortices and Thermohydrodynamic Properties

Quantized vortices in liquid ⁴ He are treated quantum mechanically with realistic many-body model wave functions in variational calculations for energy and core structure at T = 0 K. A rectilinear vortex and both small and large vortex rings are studied. Calculated results indicate that rotons are not just small-quantized vortex rings. We compare our results for quantized vortices with experimental data and with theoretical results calculated by others. Correlated basis functions and standard statistical mechanics are used in treating thermohydrodynamic properties of flowing liquid ⁴ He. The Helmholtz potential is evaluated for a model of the flowing liquid that includes phonons and interacting rotons. Characteristics of this potential are discussed. The physical nature of negative superfluid density is explained. Superfluid density, entropy, and specific heat for liquid He-II are evaluated using our theory and the results are compared with experimental data. Very good agreement is found, except in a small temperature range near the λ transition. We indicate that results obtained here can be used in extending the theory to include thermally excited vortices and to investigate the possible role of vortices in accounting for the λ transition in liquid ⁴ He.      

Time-of-Flight Experiments of Vortex Rings Propagating from Turbulent Region of Superfluid 4He at High Temperature

We report the time-of-flight of quantized vortex rings generated by a vibrating wire in superfluid ⁴He which contains normal fluid component. A cover box of vibrating wires and slow cooling of superfluid reduce the number of vortices attached to wire surfaces, enabling us to study vortex rings propagating from a turbulent region. Using two vibrating wires as a generator and a detector of vortices, the time-of-flight of vortices propagating a distance of 0.88 mm was measured at 1.25 K. We find that the time-of-flights distribute from 0.06 s to 27.4 s, much larger than the lifetimes of circular vortex rings limited in the size of a generator amplitude. These results imply that large vortex rings with non-circular shape or vortex tangles are created by the generator, propagating slowly and colliding with the detector before complete disappearance.     

Propagation of Quantized Vortices Driven by an Oscillating Sphere in Superfluid 4He

We performed numerical simulation of quantum turbulence at 0 K generated from remnant vortices attached to an oscillating sphere. The remnant vortices are extended by the sphere motion and form a tangle with emitting vortex loops. As time passes, the length of vortices in a computational volume becomes statistically steady. We investigate in the statistical steady state the distribution of the length of vortex loops and anisotropy of their propagation direction caused by the sphere oscillation. The propagation direction of the emitted vortex loops is anisotropic along the oscillation direction of the sphere. The obtained results are consistent with results obtained in the experimental study using vibrating wires in superfluid ⁴He.     

Liquid 4He: Contributions to First Principles Theory. II. Quantized Vortices and the λ Transition

Quantized vortices in liquid ⁴He at finite temperatures are treated by first principles theory that extends results presented in paper I of this two-part set. Then the possible role of thermally excited quantized vortices in accounting for the λ transition is studied. This study indicates that vortices are probably not the dominant mechanism responsible for the λ transition, but that they may account for some minor effects near T _λ . A model that identifies critical fluctuations with quantized isothermal fourth sound waves is developed and used to derive formulas for specific heat in He II and He I. Logarithmic divergence of the constant volume specific heat is found. Numerical calculations using those formulas produce close agreement with experimental data. A formula for the radial distribution function near T _λ in He II and He I is derived and numerically evaluated. A formula for the correlation length is derived and numerically evaluated and physical characteristics of the correlation length are discussed. Numerical calculations based on that formula for correlation length are compared with experimental results. Long-range order in the liquid exhibited in the radial distribution function and correlation length is shown not to involve a Bose-Einstein condensate in this theory. The isothermal compressibility is found by integration of the radial distribution function and the result shows that isothermal compressibility is unchanged by critical fluctuations of isothermal fourth sound.     

Textures and Exotic Vortices in Neutral Fermion Superfluids

There has been intense interest in various Fermion superfluids in neutral atom liquids and gases, including chiral p-wave pairing in ³He-A phase and Feshbach-resonanced ⁶Li atom gases and d-wave pairing in atom gases. It is particularly interesting to find exotic vortices and associated low-lying Fermionic excitations under rotation. Here we report on our efforts of those topics: (1) Majorana Fermion in chiral superfluids near a p-wave Feshbach resonance. (2) Possible half-quantum vortices in p-wave superfluids of trapped Fermion atom gases. (3) Stability of a half-quantum vortex in rotating superfluid ³He-A between parallel plates. (4) Majorana bound state in rotating superfluid ³He-A between parallel plates. (5) Non-Abelian Fractional vortex in d-wave Feshbach resonance superfluids. We will summarize some of those works in a coherent manner in order to bridge the understanding between cold atom community and superfluid ³He community by stressing the importance of cross fertilization between them.     

Observation of Remanent Vortices Attached to Rough Boundaries in Superfluid 4He

We report the study on remanent vortices attached to rough boundaries in superfluid ⁴He after the turbulent transition. We used 2.6 µm vibrating wires with smooth surfaces and rough surfaces, a cover box and slow cooling method, in order to investigate the effect of surface roughness on the condition and the number of vortices attached to a wire. The responses of the wire with smooth surfaces show large hysteresis at the turbulent transition. This result indicates that remanent vortices attached between the wire and surrounding boundaries cause turbulence. At first sweep of driving force of the wire with rough surfaces, we also observed hysteresis as large as the case of the smooth wire: at the other sweeps, however, small hysteresis was observed. These results indicate that once turbulence is generated at a wire velocity during first sweep, vortex lines newly attach between rough surfaces of the wire, which easily cause turbulence at a low wire velocity. Therefore, we conclude that a smooth wire can reduce the number of vortices attached to a wire.     

Vortices and Dynamics in Trapped Bose-Einstein Condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schrödinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid ⁴He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.     

Transition to Quantum Turbulence and the Propagation of Vortex Loops at Finite Temperatures

We performed numerical simulation of the transition to quantum turbulence and the propagation of vortex loops at finite temperatures in order to understand the experiments using vibrating wires in superfluid ⁴He by Yano et al. We injected vortex rings to a finite volume in order to simulate emission of vortices from the wire. When the injected vortices are dilute, they should decay by mutual friction. When they are dense, however, vortex tangle are generated through vortex reconnections and emit large vortex loops. The large vortex loops can travel a long distance before disappearing, which is much different from the dilute case. The numerical results are consistent with the experimental results.     

Dynamics of a Particle and a Quantized Vortex at Zero Temperature: Self-consistent Calculation

Many experiments for visualizing quantized vortices and normal fluid flow have been performed in superfluid ⁴He. Recently, metastable He₂ excimer molecules have been used as tracer particles. Since their radius is only about 10^?10 m, they hardly perturb the system, thus being a good candidate of tracer particles. In order to understand the interactive motion of He₂ molecules and vortices at zero temperature, we numerically study the trapping diameter by using the self-consistent equations of motions. We calculated the trapping diameter as a function of the initial velocity of the particle. The trapping diameter is almost inversely proportional to the initial velocity of the particle and compared with the observation.     

Observations of Vortex Emissions from Superfluid 4He Turbulence at High Temperatures

An immersed object with high velocity oscillations causes quantum turbulence in superfluid ⁴He, even at very low temperatures. The continuously generated turbulence may emit vortex rings from a turbulent region. In the present work, we report vortex emissions from quantum turbulence in superfluid ⁴He at high temperatures, by using three vibrating wires as a turbulence generator and vortex detectors. Two detector wires were mounted beside a generator wire: one in parallel and the other in perpendicular to the oscillation direction of the generator. The detection times of vortex rings represent an exponential distribution with a delay time t ₀ and a mean detection period t ₁. The delay time includes the generation time of a fully developed turbulence and the time-of-flight of a vortex ring. At high temperatures, vortices are dissipated by relative motion between a normal fluid component and the vortices, resulting that only large vortex rings are reachable to the detectors. Using this method, we detected vortex rings with a diameter of 100 μm, comparable to a peak-to-peak vibration amplitude of 104 μm of the generator. The large vortices observed here are emitted anisotropically from the generator. The emissions parallel to the vibrating direction are much less than those perpendicular to the direction.     

On the Visualization of Thermal Counterflow of He II Past a Circular Cylinder

Thermal counterflow of superfluid ⁴He is investigated experimentally in the proximity of a 3 mm diameter cylinder by analyzing the motions of micrometer-sized solid particles, focusing especially on the occurrence of macroscopic vortices. The influence of heating an opaque brass cylinder by the light source is studied, as thermal counterflow is generated from its surface, and compared with the case of a transparent plexiglass cylinder of the same size. Additionally, we report our preliminary investigation of vertical counterflow around the transparent cylinder. We find that care should be taken when applying conventional visualization techniques—particle image velocimetry and particle tracking velocimetry—as spurious vortical structures might be identified in quantum flows displaying two-fluid behavior.     

Infrared Absorption and Emission Spectrum of Electron Bubbles Attached to Linear Vortices in Liquid 4He

Within finite-range density-functional theory, we have addressed the infrared absorption and emission spectrum of electron bubbles attached to linear vortices in liquid ⁴He as a function of pressure. We have found that the presence of vortices affects very little the absorption spectrum, only causing a small shift in the 1s→2p peak. The energy of the lowest emission transition is also shown as a function of pressure for a vortex-free bubble and for a trapped bubble. In the emission energy the shift induced by the vortex line is proportionally bigger, especially when the waist around the electron probability density of the 1p state collapses, which happens at a pressure of ～8 bar.     

Experiments on a High Quality Grid Oscillating in Superfluid 4He at Very Low Temperatures

We have investigated a copper-mesh grid oscillating at its fundamental (0, 1) Bessel mode in superfluid ⁴He for temperatures 10<T<1500 mK at a pressure of P=5 bar. The high quality factor (Q～10⁵) of the oscillator allowed us to observe new features of its response to a periodic drive which, at the lowest T, was found to depend on the prehistory of the helium. The experiments have confirmed the existence of two critical velocities, and we discuss whether these critical velocities are associated with quantized vortices.     

The Annealing Process in Solid 4He

We have used a torsional oscillator with square cross section and a resonance frequency of 185 Hz to confirm the nonclassical rotational inertia (NCRI) discovered by Kim and Chan (Nature 427:225, 2004; Science 305:1941, 2004). We have also found a strong correlation between the NCRI signal and a high dissipation Q ^?1 of 4×10^?6 of the oscillation above the transition temperature. Here, we present preliminary results of the annealing process in ⁴He at a pressure of 26 bar. When holding the temperature constant above 1 K we have observed a immediate rise in the period and a slow decay of the dissipation. The equilibrium value of Q ^?1 decreases with increasing temperature.     

Defects and Glassy Dynamics in Solid 4He: Perspectives and Current Status

We review the anomalous behavior of solid ⁴He at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in ⁴He. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid ⁴He. Our proposed glass model for solid ⁴He has several implications: (1) The anomalous properties of ⁴He can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid ⁴He is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich ⁴He crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in ⁴He.     

Decay of Counterflow Quantum Turbulence in Superfluid 4He

We have simulated the decay of thermal counterflow quantum turbulence from a statistically steady state at T=1.9 K, with the assumption that the normal fluid is at rest during the decay. The results are consistent with the predictions of the Vinen equation (in essence the vortex line density decays as t ^?1). For the statistically steady state, we determine the parameter c ₂, which connects the curvature of the vortex lines and the mean separation of vortices. A formula connecting the parameter χ ₂ of the Vinen equation with c ₂ is shown to agree with the results of the simulations. Disagreement with experiment is discussed briefly.     

Experiments on two immiscible fluids in spherical Couette flow

This paper deals with the experimental instabilities analysis of spherical Couette flow. We consider the flow of two immiscible fluids superimposed between concentric spheres when the outer sphere is fixed and the inner one rotates. The working fluids have rather different viscosities and thus different Reynolds numbers. The obtained results are compared with a reference case of filled gap using one fluid (Γ _max = 20). Experiments are performed for different aspect ratio values, and Laser photometric technique is used for visualization. Our analysis is mainly focused on the type of instabilities and their relationship with the laminar-turbulent transition regime. We intend to explore the combined effects of the aspect ratio and the interaction between the two superposed fluids on the appearance of different instability evolutions. The evolution of the phase velocity for different aspect ratio of heavy fluid Γ _HF = H _HF/d is presented. The immiscible fluids are separated by a liquid–liquid interface (water–oil). In order to control instability occurrence, Taylor number variation is presented versus aspect ratio. Instability phenomena are found to be the same as for the nominal case for large heavy fluid aspect ratios. The first equatorial symmetry breaking of the flow is observed for a critical value Γ _c  = 13 where the Taylor vortex flow is introduced with three stationary cells. For the same aspect ratio, the interaction of the immiscible fluids leads to the appearance of gravitational waves near the equatorial zone. A surface cell, starting before the appearance of Taylor vortices, is detected in the light fluid for low aspect ratios. This cell of Ekman type has not been observed before, to our best knowledge, in spherical Couette flow.     

Dispersion of the linear and nonlinear optical susceptibilities of disilver germanium sulfide from DFT calculations

The dispersion of the linear and nonlinear optical susceptibilities is calculated for disilver germanium sulfide (Ag₂GeS₃) using the all-electron full potential linearized augmented plane wave (FP-LAPW) method. Calculations are performed with four exchange correlations namely local density approximation (LDA), general gradient approximation (GGA), Engel–Vosko generalized gradient approximation (EVGGA), and modified Becke–Johnson potential (mBJ). Our calculations give a band gap of 0.40 eV (LDA), 0.42 eV (GGA), 1.03 eV (EVGGA), and 1.30 eV (mBJ) in comparison with our measured gap (1.98 eV). The mBJ exchange correlation gives the best agreement with experiment. We find that the calculated linear optical susceptibilities of Ag₂GeS₃ show considerable anisotropy which is useful for second harmonic generation and optical parametric oscillation. To analyze the spectra of the calculated χ ₁₁₃ ⁽²⁾ (ω), χ ₂₃₂ ⁽²⁾ (ω), χ ₃₁₁ ⁽²⁾ (ω), χ ₃₂₂ ⁽²⁾ (ω), and χ ₃₃₃ ⁽²⁾ (ω), we have correlated the features of these spectra with the features of ?₂(ω) spectra as a function of ω/2 and ω. From the calculated dominant component |χ ₃₃₃ ⁽²⁾ (ω)|, we find that the microscopic second-order hyperpolarizability, β₃₃₃, the vector components along the dipole moment direction is 41.2 × 10^?30 esu at static limit and 222.9 × 10^?30 esu at λ = 1064 nm.     

Influence of Particle Size and Heating Rate on Decomposition of BC Dry Chemical Fire Extinguishing Powders

Pyrolysis of BC dry chemical fire extinguishing powders which are useful for Class “B” and Class “C” fires was conducted on a thermogravimetric analyzer with sample loading of 10–25 mg under dynamic air atmosphere. The effect of particle sizes (medium value 48.99, 27.24, 4.93 µm) and heating rates (10, 15, and 20°C min^?1) were examined. The pyrolysis kinetics of the samples was analyzed using a distribution activation energy model. It was found that the decomposition temperature decreased and the pyrolysis rate increased after the samples were milled. The agglomeration of particles during production did not have an appreciable influence on the pyrolysis process of the samples in our experimental conditions. The activation energy value was 77.13?219.78 kJ · mol^?1, 58.18?288.67 kJ · mol^?1, and 44.59?209.17 kJ · mol^?1 for the powder of particle size 48.99, 27.24, 4.93 µm. We should use micro powder in fire extinguishing.     

Mass Flow through Solid 4H

We continue our solid ⁴He flow experiments in which we grow solid helium samples at constant temperature in the hcp region of the phase diagram. We exploit the properties of liquid helium in a confined geometry (porous Vycor glass), and induce a mass flow through the solid at pressures higher than the bulk melting pressure. We previously observed flow, but our temperature was limited to T≥350 mK. At T≈400 mK it was found that the flow ceased at P≈27 bar, and no flow was observed for T>550 mK. We have begun to extend our measurements to lower temperatures, and our data show that at lower temperatures we observe flow at higher pressures.