Superfluid Film Research Articles

Surface excitations and partial entropy of third sound in 4He

The hydrodynamics of third sound in superfluid 4He films passes through a regime dominated by surface excitations as the temperature is lowered. With a limited spatial extent, such excitations decouple from the thermomechanical forces operating within the context of the two-fluid model. This phenomenon is the basis of the "partial entropy" of Bergman's classic development of third sound hydrodynamics [1], but its distinction from entropy has been lost by subsequent authors. We present a computational example of its hydrodynamic significance and discuss the consequences for the thermomechanical aspects of third sound.

QCM study of superfluid transition in 4He films adsorbed in SBA-15

A quartz crystal microbalance (QCM) is a useful tool to study the superfluidity of 4He films at very high frequencies. Our recent efforts to fabricate mesoporous silica films onto QCM have enabled us to study the noble superfluidity adsorbed in nanopores. In this paper we report results of QCM measurements for the superfluid 4He films in SBA-15 with one-dimensional nanopores 4.1 nm in diameter and ∼ 1 μM in length. From the 4He pressure isotherm at 4.2 K, a uniform layer is formed in the nanopores up to the coverage of 48 μmol/m2, corresponding to ∼ 2.5 layers. The superfluid response is measured at 12 MHz for various coverages in the temperature range of 0.1 — 1.5 K. Above the onset coverage of ∼ 23 μmol/m2, we observed a frequency shift accompanied by a dissipation peak due to the superfluid Kosterlitz-Thouless (KT) transition.

Parallel-plate capacitor measurements of the superfluid wall-film thickness in a 3He/4He mixture of 3He mole fraction x = 0.75

A thin 4He-rich superfluid film coats solid surfaces in contact with bulk normal liquid 3He/4He mixtures in a narrow region of the mixture phase diagram at saturated vapor pressure that adjoins the lambda line, the tricritical point, and the 3He-rich branch of the phase-separation curve. Recent arguments suggest that near the tricritical point, the thickness of the film is governed not only by van der Waals forces and gravity but also by Casimir and Helfrich forces that limit the thickness as the phase-separation curve is approached. Experimental evidence has been presented both showing and failing to show this phenomenon.In the present work, parallel-plate capacitor measurements of a mixture having a 3He mole fraction x = 0.75 show a film thickness of from ∼ 14 to ∼ 22 nm as the phase-separation curve is first reached from higher temperature, depending on choice of background subtraction, whereas van der Waals forces limited only by gravity would be expected in our cell to yield a thickness of ∼ 31 nm, rising in the first few mK below the phase-separation temperature to ∼ 43 nm. Despite various uncertainties and anomalies, the results suggest that additional forces may be at work.

AN APPROXIMATION OF THE KINETIC ENERGY OF A SUPERFLUID FILM ON A RIEMANN SURFACE

The flow of a superfluid film adsorbed on a porous medium can be modeled by a meromorphic differential on a Riemann surface of high genus. In this paper, we define the mixed Hodge metric of meromorphic differentials on a Riemann surface and justify using this metric to approximate the kinetic energy of a superfluid film flowing on a porous surface.

Symmetric And Nonsymmetric Solutions For a Class of Quasilinear Schrödinger Equations

Abstract We use the mountain-pass theorem combined with the principle of symmetric criticality to establish multiplicity of solutions for the class of quasilinear elliptic equations -Δu + V(z)u - Δ(u2)u = h(u) in ℝN where N ≥ 4, the potential V : ℝN → ℝ is positive and bounded away from zero and satisfies appropriate periodic and symmetric conditions. The nonlinear term h(u) has subcritical growth and satisfies a condition of the Ambrosetti-Rabinowitz type. Schrödinger equations of this type have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.

Quantized spin Hall effect inH3e-A and other p-wave paired Fermi systems

In this paper we propose the quantized spin Hall effect (SHE) in the vortex state of a rotating p-wave paired Fermi system in an inhomogeneous magnetic field and in a weak periodic potential. It is the three dimensional extension of the spin Hall effect for a 3He-A superfluid film studied in Ref. [1]. It may also be considered as a generalization of the 3D quantized charge Hall effect of Bloch electrons in Ref. [2] to the spin transport. The A-phase of 3He or, more generally, the p-wave paired phase of a cold Fermi atomic gas, under suitable conditions should be a good candidate to observe the SHE, because the system has a conserved spin current (with no spin-orbit couplings).

Dynamics of coreless vortices and rotation-induced dissipation peak in superfluid films on rotating porous substrates

We analyze dynamics of 3D coreless vortices in superfluid films covering porous substrates. The 3D vortex dynamics is derived from the 2D dynamics of the film. The motion of a 3D vortex is a sequence of jumps between neighboring substrate cells, which can be described, nevertheless, in terms of quasi-continuous motion with average vortex velocity. The vortex velocity is derived from the dissociation rate of vortex-antivortex pairs in a 2D film, which was developed in the past on the basis of the Kosterlitz-Thouless theory. The theory explains the rotation-induced dissipation peak in torsion-oscillator experiments on $^4$He films on rotating porous substrates and can be used in the analysis of other phenomena related to vortex motion in films on porous substrates.

Soliton solutions for quasilinear Schrödinger equations involving supercritical exponent in $\mathbb R^N$

We study the existence of positive solutions to the quasilinear elliptic problem <p align="center"> $-\epsilon \Delta u+V(x)u-\epsilon k(\Delta(|u|^2))u=g(u), \quad u>0,x \in \mathbb R^N,$ <p align="left" class="times"> where g has superlinear growth at infinity without any restriction from above on its growth. Mountain pass in a suitable Orlicz space is employed to establish this result. These equations contain strongly singular nonlinearities which include derivatives of the second order which make the situation more complicated. Such equations arise when one seeks for standing wave solutions for the corresponding quasilinear Schrödinger equations. Schrödinger equations of this type have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.

Critical Casimir effect in superfluid wetting films

Recent experimental data for the complete wetting behavior of pure 4He and of 3He-4He mixtures exposed to solid substrates show that there is a change of the corresponding film thicknesses L upon approaching thermodynamically the lambda transition and the tricritical end point, respectively, which can be attributed to critical Casimir forces fC. We calculate the scaling functions theta of fC within models representing the corresponding universality classes. For the mixtures our analysis provides an understanding of the rich behavior of theta deduced from the experimental data and predicts the crossover behavior between the tricritical point and the lambda transition of pure 4He which are connected by a line of critical points. The formation of a "soft-mode" phase within the wetting films gives rise to a pronounced maximum of fC below the tricritical point as observed experimentally. Near the tricritical point we find logarithmic corrections approximately L(-3)(ln L)1/2 for the leading behavior of theta dominating the contributions from the background dispersion forces.

Superfluidity of 4He Adsorbed on Nanoporous Activated Carbon Fibers

4He confined in nanoporous media is one of the most interesting nano-sized systems in the context of an interacting Bose system. In the present work, we study superfluidity of 4He adsorbed in nanoporous activated carbon fibers (ACFs). Up to a 4He coverage of n=22.6 μmol m−2, no superfluidity is observed. Over 23.7 μmol m−2, superfluid transition is observed at Tc∼550 mK. With an increase in n the superfluid density enhances, but Tc is independent of n. These observations indicate that the thickness of the superfluid 4He films on the pore wall is restricted by a slit type pore shape of ACFs.

Al/Au Bilayer Thermometer for Third Sound Detection

We present results from an experiment to develop bilayer metallic films of Al and Au as superconducting transition edge thermometers for the detection of third sound waves in thin superfluid 4He films. We compare transition edge data for such an Al/Au thermometer to that for a pure Zn thermometer and document its utility for third sound detection.

THEORY OF THIRD SOUND AND STABILITY OF THIN 3He–4He SUPERFLUID FILMS

In this paper, we summarize the results of recent studies of third sound in thin, superfluid 3 He -4 He mixture films and the relation of the third sound spectrum to the question of the films' thermodynamic stability. We have considered films on several representative substrates: Nuclepore, glass, Li and Na . Our approach utilizes the variational, hypernetted chain/Euler-Lagrange (HNC–EL) theory as applied to inhomogeneous boson systems to calculate chemical potentials for both the 4 He superfluid film and the physisorbed 3 He . Numerical density derivatives of the chemical potentials lead to the sought-after third sound speeds. On all substrates, the third sound speeds show a series of oscillations as a function of film coverage that is driven by the layered structure of the 4 He film. We find that the effect on the third sound response of adding a small amount of 3 He to the 4 He film can depend sensitively on the particular 4 He film coverage. The third sound speed can either increase or decrease. In fact, in some regimes, the added 3 He destabilizes the film and can drive "layering transitions" leading to quite complicated geometric structures of the film in which the outermost layer consists of phase–separated regimes of 3 He and 4 He . Finally, we examine the range of applicability of the usual film–averaged hydrodynamic description. We find that at least up to film thicknesses of six liquid layers, there is no regime in which this hydrodynamic description is applicable.

Recent progress in the development of a polarized proton target for reactions with radioactive ion beams

Polarization observables in nuclear reactions with stable beams have provided important information concerning structural properties of nuclei and reaction mechanisms and hold great promise in the context of exotic nuclei. We report on the development of a polarized target based on plastic foils of 20–200μm thickness to be used with radioactive ion beams. The operation of such a target requires a moderately high magnetic field and very low temperatures. The plastic foil is placed inside a chamber attached to the mixing chamber of a 3He–4He dilution refrigerator. Cooling of the foil is achieved via a superfluid film of 4He that can be supplied through two capillaries. The chamber has two thin, highly uniform silicon nitride windows. An NMR coil is attached to the target to monitor the polarization. Results of a first test to characterize the target system, using the elastic scattering of 38MeV 12C by protons in inverse kinematics are presented.

Crystalline Order in SuperfluidHe3Films

We predict an inhomogeneous phase of superfluid (3)He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, D(c2)(T) < D < D(c1)(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D(c2) approximately 9 xi (T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at D(c1) approximately 13 xi (T).

On a class of periodic quasilinear Schrödinger equations involving critical growth in [formula omitted

We consider the equation − Δ u + V ( x ) u − k 2 ( Δ ( | u | 2 ) ) u = g ( x , u ) , u > 0 , x ∈ R 2 , where V : R 2 → R and g : R 2 × R → R are two continuous 1-periodic functions and k is a positive constant. Also, we assume g behaves like exp ( β | u | 4 ) as | u | → ∞ . We prove the existence of at least one weak solution u ∈ H 1 ( R 2 ) with u 2 ∈ H 1 ( R 2 ) . The mountain pass in a suitable Orlicz space together with the Trudinger–Moser inequality are employed to establish this result. Such equations arise when one seeks for standing wave solutions for the corresponding quasilinear Schrödinger equations. Schrödinger equations of this type have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.

Experimental tests and modeling of the optimal orifice size for a closed cycle 4He sorption refrigerator

Closed cycle 4He sorption refrigerators are an increasingly popular choice for remote cryogenic operations. The presence of a superfluid film on the inner walls of the evaporation pot limits their performance. We present a simple model of the gas, film, and heat flow in a 4He sorption refrigerator, taking into account the effects of an orifice to limit superfluid film flow. The model serves as a useful guideline for optimizing cryogenic performance. We also present a diagram of hold time vs. steady state temperature as a function of the radius of the orifice and compare the model to measurements.

Critical Casimir Force inHe4Films: Confirmation of Finite-Size Scaling

We present new capacitance measurements of critical Casimir force-induced thinning of 4He films near the superfluid transition, focused on the region below Tlambda where the effect is the greatest. 4He films of 238, 285, and 340 A thickness are adsorbed on atomically smooth, N-doped silicon substrates. The Casimir force scaling function theta, deduced from the thinning of these three films, collapses onto a single universal curve, attaining a minimum theta=-1.30+/-0.03 at x=td1/nu=-9.7+/-0.8 A1/nu. The collapse confirms the finite-size scaling origin of the dip in the film thickness. Separately, we also confirm the presence down to 2.13 K of the Goldstone or surface fluctuation force, which makes the superfluid film approximately 2 A thinner than the normal film.

Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in [formula omitted

Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in R N . These equations contain strongly singular nonlinearities which include derivatives of the second order. Such equations have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.

Third sound and stability of thinHe3−He4films

We study third sound in thin $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixture films from first-principles, microscopic theory and compare these results to the usual film-averaged, hydrodynamic approach. The hydrodynamic approach yields third-sound speeds that depend only on the thickness of the superfluid film and the distribution of impurities---i.e., $^{3}\mathrm{He}$. In very thin films, this result clearly must be modified to account for the effects of nonuniform $^{4}\mathrm{He}$ film density. Utilizing the variational, hypernetted-chain--Euler-Lagrange theory as applied to inhomogeneous boson systems, we calculate accurate chemical potentials for both the $^{4}\mathrm{He}$ superfluid film and the physisorbed $^{3}\mathrm{He}$. Numerical density derivatives of the chemical potentials lead to the sought-after third-sound speeds that clearly reflect a layered structure of at least seven oscillations. We are thus able to gauge the range of applicability of the film-averaged hydrodynamic results as applied to thin quantum liquid films. We study third sound on two model substrates: Nuclepore and glass. We compute the change in third-sound speed as a function of $^{3}\mathrm{He}$ coverage in the linear (low-concentration) regime, which is then studied for the two substrates as a function of $^{4}\mathrm{He}$ film thickness and compared to existing experiments.$^{3}\mathrm{He}$ density profiles are calculated as a function of $^{4}\mathrm{He}$ film thickness, and we show explicitly the smooth transition from Andreev states in the thick-film limit to lateral mixtures in the submonolayer limit. This effect was first seen by Noiray et al. [Phys. Rev. Lett. 53, 2421 (1984)]. Our results predict that the addition of a small amount of $^{3}\mathrm{He}$ can increase, as well as decrease, the third-sound speed relative to that of the pure $^{4}\mathrm{He}$ film. Further, we show that the addition of a small amount of $^{3}\mathrm{He}$ can destabilize the film and drive a phase separation into lateral regions of $^{3}\mathrm{He}$-rich and $^{3}\mathrm{He}$-poor patches. This latter result may help explain the phase transitions reported by Bhattacharyya and Gasparini [Phys. Rev. Lett. 49, 919 (1982)] and Cs\'athy, Kim, and Chan [Phys. Rev. Lett. 88, 045301 (2002)] in thin mixture films.

On the existence of standing wave solutions to quasilinear Schrödinger equations

The fibreing method is employed to prove the existence of at least one or sometimes two standing wave solutions for quasilinear Schrödinger equations. These equations contain singular nonlinearities which include derivatives of the second order. Such equations have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.