Analog of Kelvin-Helmholtz instability on a free surface of a superfluid liquid

We analyze the analog of the Kelvin-Helmholtz instability on the free surface of a superfluid liquid. This instability is induced by the relative motion of superfluid and normal components of the same liquid along the surface. The instability threshold is found to be independent of the value of viscosity, but turns out to be lower than in the absence of dissipation. The result is similar to that obtained for the interface between two sliding super-fluids (with different mechanisms of dissipation) and confirmed by the first experimental observation of the Kelvin-Helmholtz instability on the interface between ³He-A and ³He-B by Blaauwgeers et al. (cond-mat/0111343).     

Kelvin-Helmholtz instability in anisotropic superfluids

Motivated by recent theoretical and experimental interest in the subject, we derive the condition of interfacial Kelvin-Helmholtz instability for a system of two flowing superfluids (one sliding on the other). The tensor structure of superfluid densities in anisotropic superfluids, such as ³He-A and also ³He-B under an external magnetic field, is properly taken into account. The consequences relevant to experiments on the A–B phase boundary in superfluid ³He are discussed.     

Black-hole horizon and metric singularity at the brane separating two sliding superfluids

An analogue of a black hole can be realized in the low-temperature laboratory. The horizon can be constructed for “relativistic” ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, ³He-A and ³He-B, sliding along each other without friction. A similar experimental arrangement was recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] corresponds to the appearance of the ergoregion for ripplons. In the modified geometry, this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity—the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.     

Currents in superfluid 3He

In the Ginsburg-Landau region the hydrodynamic variables for superfluid ³He are defined by means of the Lie algebra of the gauge group SO(3) x SO(3) x U(1) for the order parameter. The equilibrium of two different superfluid phases of ³He is considered within the framework of this method. At the surface, dividing the two regions filled with these phases, we consider joint conditions on currents and topological structures.     

Shear flow and Kelvin-Helmholtz instability in superfluids

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.     

Kelvin-Helmholtz instability in a rotating ideally conducting inhomogeneous plasma

The Kelvin-Helmholtz instability in sheared magnetohydrodynamic flow of an ideally conducting rotating inhomogeneous compressible plasma is investigated. The asymptotic behaviour inx of the Kelvin-Helmholtz eigenfunctions for the case of finite compressibility in the presence of rotation is discussed and instability condition is derived. In the incompressible limit, a dispersion relation is derived which has been solved numerically and discussed in detail. It is found that the inhomogeneous system is unstable in an incompressible plasma.     

Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Energy spectra of quantum turbulence in He II and 3He-B: A unified view

Quantum turbulence in superfluid He II and in ³He-B that can be regarded as nearly isothermal, isotropic, and homogeneous is discussed within the two-fluid model. A general form of the 3D energy spectrum is proposed: at large length scales, where normal and superfluid eddies are locked together by the mutual friction force, the energy spectrum is essentially classical and includes an inertial range of a Kolmogorov K62 form. With increasing wavenumber k, the normal fluid part of the spectrum terminates due to finite viscosity, while the superfluid part of the spectral energy density changes towards k ⁻³ and then back into Kolmogorov-like k ^−5/3 again. Agreement with computer simulations and experiments is claimed if account is taken of the turbulent box size and of the energy decay rate. The text was submitted by the author in English.     

Parametric instability in uniform spin precession in superfluid 3He-B

In order to explain the “catastrophic spin relaxation” observed in superfluid ³He-B, the stability of spatially uniform spin precession in this liquid relative to the parametric excitation of spin waves has been analyzed. It is shown that uniform spin precession becomes unstable at low temperatures (Suhl instability). At zero temperature, the growth increments are determined for all spin wave branches. The temperature at which the transition from stable spin precession to instability takes place is estimated.     

Critical velocity in 3He-B vibrating wire experiments as analog of vacuum instability in a slowly oscillating electric field

The Lancaster experiments [C. A. M. Castelijns, K. F. Coates, A. M. Guenault, S. G. Mussett, and G. R. Pickett Phys. Rev. Lett. 56, 69 (1986)] with a cylindrical wire moving in superfluid ³He-B are discussed, where the measured critical velocity of pair creation was much below the Landau critical velocity. The phenomenon is shown to be analogous to the instability of the electron-positron vacuum in an adiabatically alternating strong electric potential of both signs, where the positive-and negative-root levels cross and thus the instability threshold is half the conventional value in a single static potential well. Zh. éksp. Teor. Fiz. 115, 70–79 (January 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Basic connection between superconductivity and superfluidity

A basic and inherently simple connection is shown to exist between superconductivity and superfluidity. It is shown that the author's previously derived general equation, which agrees well with the superconducting transition temperatures for the heavy-electron superconductors, metallic superconductors, oxide superconductors, metallic hydrogen, and neutron stars, also works well for the superfluid transition temperature of 2.6 mK for liquid³He. Reasonable estimates are made from 10^–3 to 10⁹ K — a range of 12 orders of magnitude. The same paradigm applies to the superfluid transition temperature of liquid⁴He, but results in a slightly different equation. The superfluid transition temperature for dilute solutions of³He in superfluid⁴He is estimated to be l–10K. This paradigm works well in detail for metallic, cuprate, and organic superconductors.     

Gauge group and phases of superfluid 3He

The p-wave phases of superfluid ³He are classified without the unitary constraint or the constraints on the net nuclear magnetization and the magnetic susceptibility.     

Effects of Thermally Induced Roton-Like Excitation on the Superfluid Density of a Quasi-2D Dipolar Bose Condensed Gas

Using the Green's function approach, the density–density correlation function and the dielectric function in the random-phase approximation for a quasi-two-dimensional (quasi-2D) dipolar Bose gas are derived. From the pole of the density correlation function, by considering thermally induced roton-like excitations, the excitation spectrum of the system is calculated. It is shown that the position and depth of the roton minimum of the excitation spectrum are tunable by changing the temperature. To show how the position of the roton minimum influences the phenomenon of superfluidity, the superfluid density of the system is obtained and it is shown that the interplay of the thermal rotonization, contact and dipole–dipole interaction (DDI) can affect the superfluid fraction of a quasi-2D Bose gas. It is found that contact, DDI interactions, and thermally induced rotons enhance the fluctuations and reduce the superfluid density. In the absence of DDI and thermally induced rotons, the usual T³ dependence of superfluid density in 2D is obtained and the correction T⁴ term arises from DDI. It is shown that if the roton minimum is close to zero, the thermally induced rotons change the linear temperature dependence of the superfluid fraction, leading to a transition to nontrivial supersolid phase.     

Triplet superfluidity in neutron matter with Skyrme forces at subnuclear and supranuclear densities in a strong magnetic field

Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T _c,1(n, H) and T _c,2(n, H) (which are nonlinear functions of density, n, and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases ³He - A₁ and ³He - A₂) in steady and homogeneous sufficiently strong magnetic field (but |μ _n |H ≪ E _c < ɛ _F (n), where μ _n is the magnetic dipole moment of a neutron, E _c is the cutoff energy and ɛ _F (n)is the Fermi energy in neutron matter). General formulae for T _c,1,2(n,H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density n (at sub- and supranuclear densities) from the interval 0.7 n ₀ ≲ n < n _c (Skyrme)< 2 n ₀, where n ₀ =0.17 fm⁻³ is the nuclear density and n _c (Skyrme)is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.     

Superfluid properties of magnetized 3He-B in a disordered medium

The influence of nonmagnetic impurity scattering on the anisotropy of the magnetized B phase of superfluid ³He is investigated theoretically. The contribution of the impurity-induced spin-singlet superfluid correlations in the presence of the p-wave Cooper pairing is revealed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 95–100 (25 January 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Gravity of monopole and string and the gravitational constant in 3He-A

We discuss the effective metric produced in superfluid ³He-A by such topological objects as the radial disgyration and monopole. In relativistic theories these metrics are similar to that of the local string and global monopole, respectively. But in ³He-A they have a negative angle deficit, which corresponds to a negative mass of the topological objects. The effective gravitational constant in superfluid ³He-A, deduced from a comparison with relativistic theories, is G∼Δ⁻², where the gap amplitude Δ plays the part of the Planck energy. G depends on temperature roughly as (1−T ²/T _c ² )⁻² and corresponds to a screening of Newton’s constant. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 666–671 (10 May 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The superfluid vacuum state,time-varying cosmological constant,and nonsingular cosmological models

Some cosmological consequences of the superfluid vacuum state developed previously by the authors are discussed, particularly with regard to the initial stages of the universe. The transition temperature of the hadronic superfluid (superfluid during the hadron era) is estimated to be 10 ¹³ K, which is the same as the Hagedorn temperature, giving a physical basis of the thermodynamic bootstrap model.     

Rotational quantum friction in superfluids: Radiation from object rotating in superfluid vacuum

The friction experienced by a body rotating in a superfluid liquid at T=0 is discussed. The effect is analogous to the amplification of electromagnetic radiation and spontaneous emission by a body or black hole rotating in the quantum vacuum, first discussed by Zel’dovich and Starobinsky. The friction is caused by the interaction of the part of the liquid which is rigidly connected with the rotating body and thus represents a comoving detector, with the “Minkowski” superfluid vacuum outside the body. The emission process is the quantum tunneling of quasiparticles from the detector to the ergoregion, where the energy of quasiparticles is negative in the rotating frame. This quantum rotational friction caused by the emission of quasiparticles is estimated for phonons and rotons in superfluid ⁴He and for Bogoliubov fermions in superfluid ³He. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 4, 257–262 (25 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Surface Majorana cone of the topological superfluid 3He B phase

Topological superfluids and superconductors have been theoretically proposed, and it is now necessary to experimentally confirm their existence. Superfluid ³He should be the ideal test subject for topological theories because its bulk state is established to be that of a spin-triplet p-wave superfluid. Surface Andreev bound states of superfluid ³He were investigated by transverse acoustic impedance measurements and their linear dispersion was confirmed on a highly specular wall. The superfluid ³He B phase was found to be a topological superfluid showing bulk–edge correspondence and a surface Majorana cone was confirmed on the surface. Possible manifestations of the Majorana nature of the surface states are discussed.     

Superfluidity of 3He in aerogel at T=0 in a magnetic field

The transition of liquid ³He to the superfluid B phase in aerogel at T=0 is considered. It is shown that in a magnetic field, the quantum phase transition with respect to pressure is split in two. The amount of splitting δP is estimated. The components of the superfluid density tensor are calculated near the critical pressures. Zh. éksp. Teor. Fiz. 115, 754–762 (February 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.