Superfluid Dynamics Research Articles

Microscopic theory of sound propagation in the superfluidHe3–aerogel system

We present a theory of sound propagation in superfluid $^{3}\mathrm{He}$ confined in aerogel, taking dragged aerogel motion into account. The superfluid dynamics coupled with the aerogel motion is formulated by use of the Keldysh Green's function for weak-coupling superfluid Fermi liquid. We apply the theory to the hydrodynamic regime and calculate the attenuation of a hydrodynamic longitudinal sound mode, the so-called fast mode. The result is compared to the acoustic experiment reported by the Northwestern University group [R. Nomura, G. Gervais, T. M. Haard, Y. Lee, N. Mulders, and W. P. Halperin, Phys. Rev. Lett. 85, 4325 (2000); G. Gervais, R. Nomura, T. M. Haard, Y. Lee, N. Mulders, and W. P. Halperin, J. Low Temp. Phys. 122, 1 (2001)]. We find reasonable agreement between the theory and the experiment.

NMR in Superfluid Helium-3 in the Non-Hydrodynamic Regime

This article is dedicated to the memory of Olli Lounasmaa, the physicist, who directed my scientific life along the path of superfluid 3He! In the article I review the results of experimental and theoretical studies of superfluid 3He spin dynamics at ultralow temperatures, where the density of the normal component is virtually zero. I describe our current understanding of the phenomena of catastrophic relaxation, NMR in the Landau field and the surface instability of homogeneous precession.

Kinetic models for superfluids: a review of mathematical results

The mathematical contributions by X.G. Lu (J. Statist. Phys. 98 (5/6) (2000) 1335–1394) and by M. Escobedo et al. (Electronic J. Differential Equations, Monograph 4 (2003)) presented in this Note constitute the first stage in the understanding of the superfluid dynamics, especially of the Bose–Einstein condensation, by means of kinetic models. The Boltzmann–Nordheim equation, which is physically relevant to describe dilute quantum Bose gases, sets important mathematical problems. Nevertheless, under an unphysical truncation of the collision cross-section at low energies, it has been proved that the spatially homogeneous Cauchy problem is well-posed. Furthermore, relaxation towards equilibrium holds in a weak sense, with the appearance of a singularity in infinite time if the initial mass is supercritical, which corresponds to the formation of a Bose–Einstein condensate. To cite this article: L. Saint-Raymond, C. R. Physique 5 (2004).

Miniature Hall sensor based ac susceptometer for measurements of vortex and superfluid dynamics in superconducting films

A highly sensitive ac susceptometer has been fabricated using a commercially available thin film Hall sensor of effective area 25×25 μm2. This instrument allows measurements of superfluid density and dynamical behavior of vortices in thin film superconductors over a broad range of frequency (10 Hz–100 kHz), temperature (4.2–300 K), and ac-field amplitude (2–150 Oe), and in static magnetic field as high as 5 T collinear with the ac field. The applicability of the susceptometer has been tested on Y1Ba2Cu3O7 films of thickness as small as ∼7 nm.

Superfluid dynamics of a Bose–Einstein condensate in a periodic potential

We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in aone-dimensional periodic potential. We study, both analytically (in the tight binding limit)and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubovdispersion relation, and we introduce two different, density dependent, effective masses andgroup velocities. The Bogoliubov spectrum predicts the existence of sound waves, andthe arising of energetic and dynamical instabilities at critical values of the BECquasi-momentum which dramatically affect its coherence properties. We investigate thedependence of the dipole and Bloch oscillation frequencies in terms of an effective massaveraged over the density of the condensate. We illustrate our results with severalanimations obtained solving numerically the time-dependent Gross–Pitaevskiiequation.

Unresolved issues in spin-polarized superfluid flow dynamics

Spin (accompanied by mass) flows can be induced magnetically in its “ferromagnetic” spin-polarized superfluid 3 He A 1 phase. Observations have been made by applying magnetic field gradients across a spin filter and measuring the induced pressure gradient. There are issues which remain unresolved. An ideal static magnetic fountain effect has not been seen. The observed effect decays with a characteristic relaxation time. The relaxation time jumps by a factor of 2 near the middle of the A 1 phase. The presence of A 1/A 2 phase interface has been speculated to cause the jump. The measured relaxation time increases with the applied field up to 1.4 T . The origins of the temperature and field dependence are not understood. Planned experiments to probe these issues are described.

A time dependent density functional treatment of superfluid dynamics: Equilibration of the electron bubble in superfluid He4

Time dependent density functionals are formulated and implemented in numerical simulations of the equilibration dynamics of an excess electron in superfluid helium. Previously developed density functionals that incorporate nonlocal potential and kinetic correlations and reproduce the dispersion curve of liquid He4, are used. The electron–helium interaction is treated using pseudopotentials, after testing their accuracy in reproducing the static properties of the solvated electron bubble through its known spectroscopy. The dynamics initiated by the sudden compression of the bubble is dissected, and the results are favorably compared to classical hydrodynamics. In the near-field, the fast motion corresponds to interfacial compressional waves, followed by the slow breathing of the cavity. The far-field motion consists of a shock wave, followed by radiating sound waves. The solitonic shock wave propagates at speeds as high as 580 m/s, determined by the amplitude of excitation. The energy carried by the shock front ensures that the subsequent bubble dynamics occurs in the linear response regime. Dissipation occurs through radiation of sound during the acceleration stages of the bubble, carried by driven phonons of λ=cτ=300 Å, where c=240 m/s is the speed of sound, and τ=130 ps is the breathing period of the bubble. The interfacial waves generate traveling excitations at k=2 Å−1, high on the positive roton branch. Excitations in the roton well are not observed. The time dependent spectroscopy of the trapped electron is shown to provide a sensitive probe of the evolving dynamics by tracking the damped oscillations of the bubble, which is damped in two periods. The results are consistent with the related time-resolved experiments on He2* Rydberg electrons, and significantly different from prior estimates of the electron-bubble relaxation dynamics.

Equation for Self-Consistent Superfluid Vortex Line Dynamics

Turbulence in helium II takes the form of a disordered tangle of quantised vortex line. The existing equation of vortex dynamics used by Schwarz and others to model the evolution of the vortex tangle does not distinguish between the large scale normal fluid velocity and the local variation of the normal fluid velocity introduced by the presence of quantised vortex lines. We derive a new vortex dynamics equation which allows the local normal fluid velocity to be determined by a modified Navier–Stokes equation. Together, the two equations form a self-consistent model to determine the coupled evolution of the normal fluid and quantised vortices.

Two-Fluid Hydrodynamics in Trapped Bose Gases and in Superfluid Helium

A review is given of recent theoretical work on the superfluid dynamics of trapped Bose gases at finite temperatures, where there is a significant fraction of non-condensate atoms. One can now reach large enough densities and collision cross-sections needed to probe the collective modes in the collision-dominated hydrodynamic region where the gas exhibits characteristic superfluid behavior involving the relative motions of the condensate and non-condensate components. The precise analogue of the Landau-Khalatnikov two-fluid hydrodynamic equations was recently derived from trapped Bose gases, starting from a generalized Gross-Pitaevskii equation for the condensate macroscopic wavefunction and a kinetic equation for the non-condensate atoms.

Berry phase from vortex dynamics in BCS superconductors revisited

Motivated by a recent series of papers by Ao et al., we reconsider the Berry phase produced by an adiabatic motion of a vortex in an s-wave BCS superconductor. Avoiding the use of the gradient expansion approach which may give rise to ambiguity in the presence of vortices, we make certain assumptions which enable us to extend the methods of Goff, Gaitan and Stone, originally used in the context of superfluid dynamics of 3 He , to our vortex problem. Using the pseudo-spin representation of the BCS Hamiltonian, contributions to the Berry phase coming from each quasiparticle state constituting the ground state are added together to give a total phase proportional to n− C 0, where n≡ 1 2 ∑ pσ(1−ϵ/ ϵ 2+|Δ| 2 ) and C 0≡∑ pσΘ(−ϵ)=p 3 F /3π 2 are the superconducting and normal electron densities, respectively. We consider this to be a clear counterexample to Ao's claim that the only possible hydrodynamic transverse force exerted on a vortex is a Magnus force proportional to n. Relations to the spectral-flow phenomenology of Volovik, and a brief discussion on possible extension to the cuprate superconductors, are suggested.

Motion control of ensembles of ordered optical vortices generated on finite extent background

Vortex motion in ordered structures is analysed numerically in the frame of the 2D nonlinear Schrödinger equation. Analogies with superfluid dynamics are presented. It was found that coherent interaction of optical vortex solitons (OVSs) leads to vortex motion, which can be adequately described by the Kelvin law in superfluid dynamics for large offsets between the OVSs. Cancelation of motion in some spatial configurations of vortices and vortex lattices is observed. The possibility to steer the motion of vortex ensembles is discussed.

Kalb-Ramond coupled vortex fibration model for relativistic superfluid dynamics

The macroscopic dynamics of a rotating superfluid deviates from that of a simple perfect fluid due to the effect of vorticity quantisation, which gives rise to a substructure of cosmic string type line defects that results in a local anisotropy whereby the effective average pressure in the direction of the vortex lines is reduced below its value in lateral directions. Whereas previous descriptions of this effect have been restricted to a non-relativistic framework that is adequate for the treatment of liquid helium in a laboratory context, the present work provides a fully relativistic description of the kind required for application to rotating neutron star models. To start with, the general category of vortex fibration models needed for this purpose is set up on the basis of a Kalb-Ramond type variational principle. The appropriate specification of the particular model to be chosen within this category will ultimately be governed by the conclusions of microscopic investigations that have not yet been completed, but the results available so far suggest that a uniquely simple kind of model with an elegant dilatonic formulation should be tentatively adopted as a provisional choice so long as there is no indication that a more complicated alternative is needed.

Explicit relativistic vortex solutions for cool two-constituent superfluid dynamics.

We give a class of explicit solutions for the stationary and cylindrically symmetric vortex configurations for a ``cool'' two-component superfluid (i.e., superfluid with an ideal gas of phonons). Each solution is characterized only by a set of (true) constants of integration. We then compute the effective asymptotic contribution of the vortex to the stress-energy tensor by comparison with a uniform reference state without vortex.

DYNAMICS OF T=0 BCS CONDENSATES

Fermi-surface bosonization is used to show that the long-wavelength, T=0, dynamics of a BCS superfluid or superconductor is described by a galilean invariant non-linear time-dependent Schrödinger equation. This equation is of same form as the Gross-Pitaevskii equation for a Bose superfluid, but the “wavefunction” is not the superfluid order parameter.

Equation of state for cool relativistic two-constituent superfluid dynamics.

The natural relativistic generalization of Landau's two-constituent superfluid theory can be formulated in terms of a Lagrangian scrL that is given as a function of the entropy current four-vector ${\mathit{s}}^{\mathrm{\ensuremath{\rho}}}$ and the gradient ${\mathrm{\ensuremath{\nabla}}}_{\mathrm{\ensuremath{\rho}}}$cphi of the superfluid phase scalar. It is shown that in the ``cool'' regime, for which the entropy is attributable just to phonons (not rotons), the Lagrangian function scrL{s\ensuremath{\rightarrow},\ensuremath{\nabla}cphi} is given by an expression of the form scrL=P-3\ensuremath{\psi} where P represents the pressure as a function just of ${\mathrm{\ensuremath{\nabla}}}_{\mathrm{\ensuremath{\rho}}}$cphi in the (isotropic) cold limit. The entropy current-dependent contribution \ensuremath{\psi} represents the generalized pressure of the (nonisotropic) phonon gas, which is obtained as the negative of the corresponding grand potential energy per unit volume, whose explicit form has a simple algebraic dependence on the sound or ``phonon'' speed ${\mathit{c}}_{\mathit{P}}$ that is determined by the cold pressure function P.

CANONICALLY COVARIANT FORMULATION OF LANDAU'S NEWTONIAN SUPERFLUID DYNAMICS

The classical Landau theory of perfect (i.e. conservative) two-constituent superfluid dynamics in Newton space-time is radically reformulated in a canonical presentation that helps to reveal symmetries and conservation properties (notably those of the thermal vorticity and helicity) that are obscured in the traditional treatment. This presentation uses a four-dimensional terminology that is more concise and elegant than the traditional 3 + 1 description and that simplifies the description of transformation properties under the action of the Milne group (i.e. the nonlinear generalization of the Galilei group).

Numerical experiments on single quantized vortices

The computational approach to superfluid dynamics is outlined, and its usefulness is illustrated by application to three problems involving single quantized vortices. We consider the vortex mill in 4He channel flow, the unwinding of a vortex from a wire in 3He-B, and the phase-slip behavior of a vortex filament in a microscopic orifice.

Simulation of two-dimensional vortex dynamics

The two-dimensional XY model is simulated with a time-dependent Ginzburg-Landau type dynamics. The data are, in the limit of small driving force, well described by the Minnhagen phenomenology for vortex dynamics of a two-dimensional superfluid. This phenomenology is different and distinguishable from the conventional AHNS phenomenology. The Minnhagen phenomenology has been observed in recent experiments on Josephson-junction arrays and high- T c BSCCO films. The present simulations suggest that this reflects an intrinsic property of the vortex dynamics for a two-dimensional superfluid.

Multichannel system for fast measurement of temperatures at 1-4.2K

The report presents a set of electronics designed for investigation of fast thermal processes taking place in He I and He II. Its main features are as follows. First, temperature field is measured at several distanced points in short time. This is useful, for example, while dealing with second-sound shock waves, superfluid turbulence dynamics, etc. Second, minimal wiring is sufficient for multipoint temperature measurement what is principal, especially, in the case of forced flow cryostats. Third, the measurement procedure allows to achieve rather high precision with the use of rather low-sensitive Ge thermometers. Warm and cold tests have shown the system efficiency and reliability.

SUPERFLUID FIELD THEORY

The very low temperature dynamics of an isotropic superfluid is derived from a repulsive bosonic field theory. The field theory is a fully dynamical generalization of the Ginzburg-Landau theory, which at zero temperature has semiclassical superfluid solutions. It is shown that supercurrent quenching occurs above some intrinsic critical velocity. The speed of first sound is calculated and the Landau criterion for a maximum superfluid velocity is derived. At finite temperature, the thermodynamic potential is computed, the order parameter and gap equations are derived, the origin of the Landau two-fluid model is identified and the thermomechanical effect is explained. This theory successfully describes many of the features of 4He well below the critical temperature, as well as relativistic generalizations.