Superfluid Mixtures Research Articles

Phase Separation and Nucleation in Superfluid Mixtures of 3He–4He at Presence of a Heat Flow

The kinetics of phase separation of superfluid 3He–4He mixtures heated from below is studied. Phase separation is registered by sharp change of concentration in different parts of a measuring cell. It is shown that separation is preceded with formation of a metastable supersaturated mixture, and a temperature gradient, under which phase transition starts, practically coincides with a critical temperature gradient for occurring the thermal instability. The obtained data can be explained in the frame of the model where nucleus of a new phase are formed on quantized vortices which attract 3He in their core. The attainable value of concentration estimated within this model of the supersaturated mixture is in rather good agreement with experimental data. At the same time it is not clear yet what among the processes starts first: phase separation or thermal instability.

Coexistence and shell structures of several superfluids in trapped three-component Fermi mixtures

We study the properties of a trapped interacting three component Fermi gas. We assume that one of the components can have a different mass from the other two. We calculate the different phases of the three component mixture and find a rich variety of different phases corresponding to different pairing channels, and simple ways of tuning the system from one phase to another. In particular, we predict coexistence of several different superfluids in the trap, forming a shell structure, and phase transitions from this mixture of superfluids to a single superfluid when the system parameters or temperature is varied. Such shell structures realize superfluids with a nontrivial spatial topology and leave clear observable signatures in the density profile of the gas.

Two-fluid hydrodynamics: New aspects

Several systems described by the two-fluid model are considered. (1) For the superfluid 4He and 3He-4He mixtures, a new integral of motion is found, finite-temperature conditions for thermodynamic stability generalizing the Landau criterion for superfluidity are analyzed, and a theory of critical-velocity behavior of superflow is developed. (2) For the two-component system consisting of a lattice and a quasiparticle gas, a two-velocity elasticity theory is developed that explains linear facet growth in helium crystals. (3) For superflow in a uniform gravitational field, the hydrodynamic equations derived by invoking the equivalence principle of general relativity are used to analyze dissipative heat transfer in the Earth’s gravity field.

Temperature-dependent pulsations of superfluid neutron stars

We examine radial oscillations of superfluid neutron stars at finite internal temperatures. For this purpose we generalize the description of relativistic superfluid hydrodynamics to the case of superfluid mixtures. We show that in a neutron star at hydrostatic and beta-equilibrium the red-shifted temperature gradient is smoothed out by neutron superfluidity (but not by proton superfluidity). We calculate radial oscillation modes of neutron stars assuming frozen nuclear composition in the pulsating matter. The resulting pulsation frequencies show a strong temperature dependence in the temperature range (0.1-1) T_cn, where T_cn is the critical temperature of neutron superfluidity. Combining our results with thermal evolution, we obtain a significant evolution of the pulsation spectrum, associated with highly efficient Cooper pairing neutrino emission, for 20 years after superfluidity onset.

Hydrodynamic equations and collective modes in a system comprising a porous medium and a He3–He4 superfluid mixture

The dynamical equations are obtained for a system comprising a porous material and a He3–He4 superfluid mixture. The elastic coefficients that appear in the equations are expressed in terms of physically measurable quantities. The equations obtained describe all of the bulk modes that propagate in a porous medium filled with a He3–He4 superfluid mixture. The propagation of acoustic modes is investigated for an aerogel filled with a He3–He4 superfluid mixture. The velocities of the longitudinal modes propagating in that system are calculated, and the relations between oscillatory quantities are established.

Thermal instability of stratified superfluid mixtures 3He– 4He under heating from below

The influence of horizontal liquid motion on Kelvin–Helmholtz instability of stratification boundary in superfluid solution 3He– 4He is studied taking into account the finiteness of the upper phase rich in 3He. The temperature dependence of critical velocity is estimated as for ideal and viscous liquids.

Entrainment parameters in a cold superfluid neutron star core

Hydrodynamic simulations of neutron star cores that are based on a two-fluid description in terms of a neutron-proton superfluid mixture require the knowledge of the Andreev-Bashkin entrainment matrix which relates the momentum of one constituent to the currents of both constituents. This matrix is derived for arbitrary nuclear asymmetry at zero temperature and in the limits of small relative currents in the framework of the energy density functional theory. The Skyrme energy density functional is considered as a particular case. General analytic formulas for the entrainment parameters and various corresponding effective masses are obtained. These formulas are applied to the liquid core of a neutron star composed of homogeneous plasma of nucleons, electrons, and possibly muons in \ensuremath{\beta} equilibrium.

The entrainment matrix of a superfluid neutron–proton mixture at a finite temperature

The entrainment matrix (also termed the Andreev–Bashkin matrix or the mass-density matrix) for a neutron–proton mixture is derived at a finite temperature in a neutron star core. The calculation is performed in the frame of the Landau–Fermi-liquid theory generalized to account for superfluidity of nucleons. It is shown, that the temperature dependence of the entrainment matrix is described by a universal function independent on an actual model of nucleon–nucleon interaction employed. The results are presented in the form convenient for their practical use. The entrainment matrix is important, e.g., in kinetics of superfluid nucleon mixtures or in studies of the dynamical evolution of neutron stars (in particular, in the studies of star pulsations and pulsar glitches).

Phase separation and thermal instability of superfluid He3-He4 mixtures heated from below

The influence of phase separation on the thermal stability of superfluid He3-He4 mixtures heated from below by a heat flux with a power density Q̇ up to 20 μW/cm2 is investigated in the temperature region 100–500 mK. It is found that instability is observed only in the presence of phase separation (in the high-temperature region) even at manifestly high heat flux densities. With increasing power of the heat flux at low temperatures the system undergoes phase separation and then, on further increase of Q̇, suffers thermal instability, which is manifested in a sharp increase in the effective thermal conductivity. These effects are apparently due to the destabilizing influence of the interface between the separated phases owing to capillary effects. The values of the Rayleigh and Marangoni numbers, which characterize the influence of the buoyancy and capillary forces, respectively, in relation to each other are analyzed, and it is noted that the concentrated phase is more sensitive to the action of capillary forces.

Thermal Instability of Superfluid Phase-Separated 3He-4He Solution Heated From Below

The phase separation influence on thermal instability of 3He-4He superfluid mixtures heated from below is studied in the temperature range of 70 – 550 mK. The experiments are carried out in a cylindrical cell of 2.38 cm in diameter and 4.7 cm in height with the initial concentration of 9.8 %3He. The thermal instability is registered by observing the anomaly in the dependences of temperature and concentration gradients in the cell as a function of heat flux. The instability is shown to occur only in the phase-separated solutions. We explain this behavior by the influence of capillary effects on the interface of the two-phase liquid. The experimental results are analyzed in terms of the critical Rayleigh and Marangoni numbers.

Nonlinearity and interaction of second sound waves in superfluid 4 He‐ 3 He mixture

We present the results of studies of nonlinear second sound waves in superfluid 4He-3He mixtures. Basing on the Hamiltonian approach the coefficient of mutual interaction of second sound waves is calculated and dependence of the nonlinearity coefficients of second sound on temperature and 3He concentration is determined. It is shown that introduction of 10% of 3He impurities into superfluid He II should result in lowering of the temperature Tα at which the nonlinearity coefficient changes its sing from negative to positive from 1.88 K to 1.67 K. Thus for weak 4He-3He solutions there exists a rather wide interval of temperatures below the superfluid transition temperature Tλ, in which the nonlinearity coefficient of the second sound is negative and the shock front is formed at the trailing edge of the nonlinear second sound pulse of heating. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Relaxation and dissipative processes in the phonon–impuriton system of concentrated superfluid mixtures of He3 in He4

The effective thermal conductivity of superfluid mixtures of He3 in He4 with an initial concentration of 9.8% He3 is investigated in the temperature interval 70–500 mK. The results, together with previously available experimental data on the thermal conductivity, viscosity, and mass and spin diffusion, are analyzed in the framework of the kinetic theory of the phonon–impuriton system of superfluid mixtures. It is shown that the experimental results for all the kinetic coefficients can be described from a unified viewpoint if the corresponding impuriton–impuriton scattering times are used as adjustable parameters. The role of each relaxation process in the complex hierarchy of relaxation times is determined as a function of temperature and concentration. It is found that even in concentrated mixtures a substantial contribution to the establishment of equilibrium is made by three-phonon processes. The phonon–impuriton relaxation times are calculated by integrating over the phonon energy in the entire region where such processes are allowed.

Vortices and type-I superconductivity in neutron stars

In a recent paper by Link, it was pointed out that the standard picture of the neutron star core, composed of a mixture of a neutron superfluid and a proton type-II superconductor, is inconsistent with observations of long period precession in isolated pulsars. In the following we will show that intervortex force between the magnetic flux tubes may be attractive, resulting in a type-I (rather than type-II) superconductor. In this case the magnetic field cannot exist in the form of magnetic flux tubes, supporting Link's observation. This behavior of the system is due to the strong interaction between the proton-neutron Cooper pairs, which was previously ignored. We also calculate the critical magnetic fields ${H}_{c}$ and ${H}_{c2}$ for type-I∕II superconductors. These results also support our claim of type-I superconductivity in the cores of neutron stars.

Neutron stars as type-I superconductors.

In a recent paper by Link, it was pointed out that the standard picture of the neutron star core composed of a mixture of a neutron superfluid and a proton type-II superconductor is inconsistent with observations of a long period precession in isolated pulsars. In the following we will show that an appropriate treatment of the interacting two-component superfluid (made of neutron and proton Cooper pairs), when the structure of proton vortices is strongly modified, may dramatically change the standard picture, resulting in a type-I superconductor. In this case the magnetic field is expelled from the superconducting regions of the neutron star, leading to the formation of the intermediate state when alternating domains of superconducting matter and normal matter coexist.

Relaxation of temperature and concentration in superfluid He3–He4 mixtures. Effective thermal conductivity

The relaxation of temperature and concentration of a superfluid He3–He4 mixture with an initial molar concentration of 9.8% He3 is investigated in the temperature interval 100–500 mK for different values of the heat flux. It is shown that the kinetics of the change in temperature of the liquid can be approximated by an exponential function, and the time constants obtained depend weakly on temperature. The concentration relaxation processes are analogous to the temperature relaxation processes only in the region of the single-phase mixture, while below the phase separation temperature the change in concentration with time is of a nonmonotonic character and can be described by a superposition of two exponential functions. This kind of kinetic behavior of the mixture is explained in the framework of a simple model which illustrates the distribution of the concentration over the height of the cell at various times after a heat flux is turned on. In this case the concentration relaxation of the dilute phase consists of two processes—growth of the concentration due to the participation of He3 in the normal motion, and decline of the concentration due to the formation and growth of the concentrated phase. The data on the relaxation times are used for determining the effective thermal conductivity of the mixture; the value obtained is in agreement with a calculation done in the framework of a kinetic theory of the phonon–impurity system of superfluid mixtures.

Classification of equilibrium states and hydrodynamics of quantum Fermi-liquid mixtures with the vector order parameter

The classification of possible superfluid phases of the Fermi-liquids mixture is constructed. Thermodynamics is constructed and hydrodynamic equations of superfluid Fermi-liquid mixture with vector order parameter are derived. Thermodynamic values connected with spontaneous breaking of symmetry to phase transformations and spin rotations are presented in terms of the order parameter. A new entrainment effect connected with mutual influence of magnetic and orbital degrees of freedom is predicted. Spectra of collective excitations of the considered quantum Fermi-liquid mixture are obtained. Differences of this state from the states with scalar and tensor order parameters are considered. The cases of Galilean and relativistic invariance are considered.

Onset of Convection in Superfluid3He-4He Mixture Heated from Below

The thermal instability of 3He-4He mixtures caused by heating the liquid from below has been studied experimentally. The temperature gradients were measured which appeared in the mixture with initial concentration 9.8% of 3He below 0.5 K in the presence of different heat flows from the heater at the cell bottom. At a certain critical heat flow the effective thermal conductivity of the liquid was observed to increase sharply which was naturally attributed to the convective heat transfer. It is shown that the thermal convection develops at high temperature gradients. In this case the Rayleigh numbers exceed many orders of magnitude those for heating from above. Thus the convective instability develops in a system in which the light liquid is at the top and where no prerequisite for instability is seemingly available. The resugts obtained are analyzed in terms of the theory of convective instability in binary mixtures. It is suggested that the phase separation, of superfluid mixtures caused by a heat flow could be a destabilizing factor initiating convection. The vortex formation in superfluid helium and the related turbulent flows appearing at high temperature gradients can be another factor favourable for instability of the liquid.

Convective instability of He3–4He superfluid mixtures heated from below

The convective thermal instability of He3–4He superfluid mixtures on heating from below is studied in the temperature interval 100–500 mK in mixtures with an initial concentration of 9.8% He3. It is found that at certain critical values of the power of the heat flux in the mixture there is a change in character of the heat transfer, indicating the onset of convective heat transfer. The critical temperature gradients associated with the onset of convection correspond to Rayleigh numbers many orders of magnitude greater than the Rayleigh numbers in the heating of the mixtures from above. The results are analyzed in the framework of the theory of the convective instability of binary mixtures.

Nonlinear second-sound waves in He4–3He superfluid mixtures

The Hamiltonian formalism in two-fluid hydrodynamics is generalized to the case of He4–3He superfluid mixtures. The resulting formalism is used to calculate the amplitude of the three-wave interaction for second sound and the nonlinearity coefficient of second sound in He II with a He3 impurity. It is shown that the temperature at which the nonlinearity coefficient of the second sound changes sign from negative to positive is lowered from 1.88 to 1.7 K when a 10% He3 impurity is added to the superfluid He4. Thus for weak He4–3He solutions there exists a rather wide interval of temperatures below the superfluid transition temperature Tλ in which the nonlinearity coefficient of the second sound is negative, and the shock front is formed at the trailing edge of the nonlinear second-sound heating wave.

Critical supersaturation of superfluid 3He-4He mixtures

We report the results of our systematic study of the phase separation in supersaturated 3He-4He liquid mixtures of the 3He-dilute phase. The amount of the critical supersaturation is determined within the wide ranges of the temperature (0.4–645mK) and the pressure (1–8.5kgf/cm2). Using the data we construct the surface of critical supersaturation, Δx3, cr(T, P), which enables us to recognize almost the overall behavior of the critical supersaturation in superfluid 3He-4He mixtures. The main specific features observed are (i) below ∼10mKΔx3, cr is almost temperature-independent, (ii) above ∼10mK up to ∼500mKΔx3, cr increases with the temperature, and (iii) above ∼500mKΔx3, cr decreases smoothly with the increase of temperature down to zero at the tricritical point. We give various discussions from the viewpoint of the quantum nucleation, the classical thermal nucleation and the crossover between them.