Recent progress in the theory of rotons in superfluid4He

The excitation spectrum of superfluid ⁴ He is discussed on the basis of a shadow wave function. The potential and kinetic energies of the excitations are computed at different densities. The theory has been extended at finite temperature and we obtain the roton contribution to the radial distribution function, to the depletion of the condensate and to the dynamical structure factor S(q,). We present also the first realistic microscopic computation of the roton energy at finite T. Possible role of thermally excited vortices on rotons is considered. With a simple model we show that some discrepancies between the linewidth of the roton response in neutron and in Raman scattering can be resolved.     

Study of rotons in superfluid4He by Raman scattering

There is a long standing disagreement between neutron and Raman scattering from rotons in superfluid⁴He near T. In neutron scattering the linewidth becomes very large and the roton signal seems to disappear at T. A substantially smaller linewidth is observed with Raman scattering and the roton signal is present even at T. We have interpreted this difference (J. Low Temp. Phys. 93, 879 (1993)) as due to a modulation of the roton energy by a fluctuating local superfluid velocity due to proliferation of vorticity as T is approached. This gives rise to an extra contribution to the roton linewidth in neutron scattering but not in Raman scattering in which two rotons with almost opposite momenta are excited. We propose a test of this explanation with evanescent field Raman scattering. It has been suggested (A. Kuklov, A. Bulatov and J.L. Birman, Phys. Rev. Lett. 72, 3855 (1994)) that in such a measurement the scattering by a single roton should be measurable. In this case the presence of a fluctuating local superfluid velocity should show up as in neutron scattering and corroborate our proposal.     

The evaporation of atoms from the surface of superfluid4He by rotons

A beam of rotons is directed toward the liquid surface at normal incidence. At the surface some rotons will evaporate atoms, with a wave-vector dependant probability p(q). The kinetic energy of the evaporated atom is equal to the difference in energy between the energy of the roton and the binding energy of a⁴He atom to the surface (7.16 K). The atoms which are evaporated are detected by a bolometer above the surface. The path length of the roton in the liquid, and the atom in the vacuum, are varied by changing the liquid level in the cell. By thus changing the liquid level, we change the flight time between heater and bolometer for a given wavevector of roton. We analyse the time-of-flight spectra received by the bolometer to reveal the product n(q)p(q) where n(q) is the distribution of rotons. If we assume that n(q) reflects the temperature of the phonons in the heater used to inject the rotons, we can deduce p(q). The resulting p(q) shows an unexpected decrease towards roton minimum at q < 2.1 Å^–1.     

Solitons in superfluid 4He films

The Korteweg-de Vries (KdV) equation is derived from Landau two-fluid hydrodynamics applied to the thickness oscillation of the superfluid ⁴He film at low temperatures, where the main restoring force is van der Waals attraction from the substrate and the thermomechanical force due to phonons is a small correction. Since the usual third-sound generators and detectors are far wider than the individual solitons, the asymptotic solution of the KdV equation provided by the inverse scattering method is coarse-grained by regarding it as a continuous train of sharp pulses. The envelope so obtained still shows a singular front proportional to (t–t ₀)^–1/2, where t ₀ is the arrival time of the fastest soliton, and should therefore be observable with the appropriate experimental arrangement.     

Dispersion of ripplons in superfluid4He

The excitations of the free surface of liquid⁴He at zero temperature are studied, with special emphasis to the short wave length region. The hybridization mechanism between surface and bulk modes is discussed on a general basis, investigating the scattering of slow rotons from the surface. An accurate density functional, accounting for backflow effects, is then used to determine the dispersion of both bulk and surface excitations. The numerical results are close to the experimental data obtained on films and confirm in an explicit way the general reflection mechanism exhibited by rotons. Moreover they reveal the occurrence of a damped ripplon branch above the roton threshold.     

Static response function in superfluid4He

Rigorous lower and upper bounds for the static response function in superfluid⁴He at zero temperature are derived using a sum rule approach. The ingredients needed to calculate the bounds are taken from recent Monte Carlo simulations for the ground state. The new bounds improve significantly the Feynman approximation and provide estimates of the static response function in agreement with the experimental data at zero pressure.     

An equilibrium theory of the dilute solutions of3He in superfluid4He at very low temperatures

An equilibrium theory of the dilute solutions of ³ He in superfluid ⁴ He is derived systematically. The theory is based on a model which (a) goes beyond the parabolic Landau-Pomeranchuk approximation for the ³ He quasiparticle energy by taking into account the fourth-order term in the momentum expansion of this quantity, (b) disregards contributions to the ³ He quasiparticle effective interaction whose order in the momentum is higher than two, and (c) allows the effective interaction to be nonlocal. The simplicity of the model enables the development of a unified parametrization of the various equilibrium properties of the solutions. The expressions obtained for these properties are both easy to apply and highly accurate over a wide temperature range spanning from T=0 to temperatures of the order of the ³ He quasiparticle degeneracy temperature. It is shown that the parameters appearing in the expression for the ³ He quasiparticle effective interaction at fixed ⁴ He number density are replaced in the fixed-pressure, low-temperature expansions of the equilibrium properties by other parameters whose appearance in the theory seems to be due to the renormalization of this interaction by the interactions between the ³ He quasiparticles and the virtual fluctuations of the ⁴ He number density Finally, a comparison is made between theory and experiment. Three quantities are considered in detail : the ³ He osmotic pressure and the ³ He quasiparticle inertial and specific heat effective masses. The analysis of the experimental data makes it possible to determine the parameters associated with the effective interaction at several pressures. It is found that the theory is, in general, in a very good accord with the experimental situation and that, within its framework, the experimental values of the osmotic pressure and the two effective masses are indeed consistent with one another.     

Depression of the superfluid transition in4He

We study superfluid⁴He near T in a homogeneous metastable state where a finite superfluid velocity v_s is present. Neglecting vortices we perform a renormalization-group calculation of the critical velocity v_sc(T) at which the superfluid state becomes unstable. We apply this result to the situation where the superfluid velocity is induced by a finite heat current Q. A critical heat current Q_c(T) corresponding to v_sc(T) is found which implies a transition temperature T (Q)=T[1–A_oQ^x]. We determine the exact exponent x=[(d–1)v] ^–1 0.744 in d=3 dimensions and calculate A_o in one-loop order. Our results for A_o and x are compared with recent experimental data.     

A novel He3He4 dilution refrigerator with superfluid He4 circulation

A novel dilution refrigerator system is proposed, which offers the potentiality of very high circulation rates. The design of this refrigerator is described and the construction and performance of a prototype are discussed. He⁴ is circulated by means of a multi-stage thermomechanical or fountain pump, which can build up high fountain pressures.     

Heat transport in dilute mixtures of3He in superfluid4He

We report new measurements of the effective thermal conductivity K_eff and relaxation time τ in dilute mixtures of³He in superfluid⁴He, with molar concentrationsX≤10⁻³. The temperature range extended fromT≈1.4 K toT _λ. Both K_cff and τ are found to agree with theoretical predictions, in contrast to previous experiments where significant differences were observed. A new thermal conductivity cell design was used which almost completely eliminates extraneous volumes and surfaces, and the earlier results are explained in relation to these design changes.     

Second-viscosity phenomena in dilute solutions of3He in superfluid4He

A theory of second-viscosity phenomena in dilute solutions of³He in superfluid⁴He is presented. The theory considers only phonon and³He quasiparticle excitations and is therefore valid at temperatures below about 0.6 K. It is shown, by an exact calculation, that within the framework of the Landau-Pomeranchuck model for the³He quasiparticle excitation energy, the four second-viscosity coefficients are related to one another and that only one of them is actually an independent kinetic coefficient. The relations between the second-viscosity coefficients are applied to analyze the expressions for the dissipative function and the first- and the second-sound attenuation coefficients. It is shown that the second-viscosity contribution to the second-sound attenuation is smaller by an order of magnitude than its contribution to the first-sound attenuation.     

Multiple quantum phase slips in superfluid4He

Phase slips by 2 in the critical flow of superfluid 4He through an orifice have been known to exist for some time. Besides these small, regular events, large and precipitous drops of the velocity which may cause up to a full collapse of the flow through the orifice have been observed by a number of authors. We have found that collapses are robust and repeatable features during the same cool-down and correspond to events involving n quantized vortices. They depend on temperature, pressure, 3He content and resonator drive level. At a given pressure, their appearance is governed solely by the magnitude of the superfluid velocity vs.     

Mean free path effects in superfluid4He

The mean free path effects in superfluid He II was studied with a vibrating wire method in the temperature range from T down to 20 mK under the saturated vapour pressure. The transition from the hydrodynamic regime to the ballistic regime was clearly observed at around 0.7 K with a 47 µm diameter wire. In the hydrodynamic regime the usual Stokes' approximation was found to be insufficient to interpret the results. In the ballistic regime the results can be explained quantitatively with the kinetic theory of phonons. However, below about 0.15 K there appear non-linear effects such as the distortion of the resonance line shape and a hysteresis behavior, which become stronger with decreasing temperature.     

Theory of dilute solutions of3He in superfluid4He. I. Perturbation theory in a nonorthogonal basis

A new procedure is presented which enables the development of perturbative expansions for the energies and transition amplitudes in systems described by nonorthogonal basis functions. The procedure is based upon defining a new metric matrix, that is, by redefining the quantum-mechanical scalar product. The results justify certain previous applications of the Schmidt orthogonalization method. It is shown that the same results can be obtained using Löwdin orthogonalization. While the procedure was developed for application with the correlated basis function (CBF) approach to dilute³He-⁴He solutions, it can be applied in any nonorthogonality situation.Supported in part by the Office of Naval Research and in part by a Quinnipiac College Faculty Research Grant-in-Aid.A portion of this work has been submitted in a thesis by R.H.K. in partial fulfillment of the requirements of the Ph.D. degree to the Graduate School, University of Massachusetts, Amherst.     

Solitary waves in saturated films of superfluid 4He

It is shown that there should exist in saturated films of superfluid ⁴He at low temperature a nonlinear surface wave described by the Korteweg-de Vries equation. The effect of surface tension makes the solitary wave cold, in contrast to very thin films discussed in a preceding paper. An electrostatic method is proposed to generate cold solitary waves. The asymptotic behavior can be found theoretically by the inverse scattering method. Estimates of parameters imply the possibility of observing each solitary wave separately.     

Time-dependent thermal convection in dilute solutions of 3He in superfluid 4He

Time-dependent thermal convection can occur in a unity-aspect-ratio Rayleigh-Beard convection cell containing a dilute solution of ³He in superfluid ⁴He when the fluid is heated from above. Results are presented primarily for a 0.24 mole % He solution at 0.925 K. Means is provided for introducing heat at the top and separately for a central plug and an outer ring such that both are at a constant temperature gDT above the bottom. A critical temperature difference T _cfor convection can be defined above which both steady and time-dependent convection occur. The time-dependent effects include a region of T. near T _cand characterized only by excessive noise, a region of somewhat higher T where there are intermittent major changes in the plug heating rate with a time distribution like that for random events, and a region at still higher T where periodic but nonsinusoidal variation of the heat flow is observed. When a long enough time, several months, has elapsed after cooling down the apparatus, time-dependent states no longer occur, and the heat flow above T _cis limited to steady convection. Briefly raising the temperature of the apparatus to 77 K is sufficient to restore the possibility of time-dependent states.     

Spreading of superfluid4He on MgF2

We have investigated the spreading of superfluid⁴He on top of a polished fused silica plate which is coated by a thin layer of MgF₂. Our interferometric experiments indicate that a superfluid⁴He film of about 100 nm thickness is not able to spread uniformly over a nearly horizontal substrate, and hence these films cannot be governed by the Van der Waals forces only. Even in the stationary state, we observe nonzero (1 – 20 mrad) contact angles which display hysteresis, spatial variation, and strong history dependence.