Nonlinear propagation of ultrasound in superfluid3He

After introducing the physics of sound propagation in normal and superfluid³He, nonlinear phenomena are discussed. These bear close resemblance to optical effects, including saturation of the absorption, amplitude dependence of the group velocity, pulse break-up, and pulse compression. Preliminary evidence indicates that above an input power threshold the sound pulses propagate in a solitonlike fashion. A naive sine-Gordon model does not explain the observations.     

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.     

Observation of magnetization reversals during relaxation measurements on superfluid 3HeA

A reversal of the recovery of the magnetization following an rf pulse has been observed in superfluid ³HeA in 306 Oe. The time difference between the end of the rf pulse and the start of the magnetization reversal is found to be proportional to both (1 ? T/T_c)^{?$\text{1}\text{2}$} and the magnitude of the initial rotation angle θ.     

Ultrasound attenuation of superfluid 3He in aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B phase of superfluid 3He in 98% porosity aerogel down to the zero temperature limit for a wide range of pressures at zero magnetic field. The absolute attenuation was determined by direct transmission of sound pulses. Compared to the bulk fluid, our results revealed a drastically different behavior in attenuation, which is consistent with theoretical accounts with gapless excitations and a collision drag effect.     

Specific heat of disordered superfluid 3He

The specific heat of superfluid 3He, disordered by a silica aerogel, is found to have a sharp discontinuity marking the thermodynamic transition to superfluidity at a temperature reduced from that of bulk 3He. The magnitude of the discontinuity is also suppressed. This disorder effect can be understood from the Ginzburg-Landau theory which takes into account elastic quasiparticle scattering suppressing both the transition temperature and the amplitude of the order parameter. We infer that the limiting temperature dependence of the specific heat is linear at low temperatures in the disordered superfluid state, consistent with predictions of gapless excitations everywhere on the Fermi surface.     

Stability problem in nonlinear wave propagation

An explicit expression for the excitation spectrum of the stationary solutions of a nonlinear wave equation is obtained. It is found that all branches of many-valued solutions of a nonlinear wave equation between the (2K+1,2K+2) turning points (branch points in the complex plane of the nonlinearity parameter) are unstable. Some parts of branches between the (2K,2K+1) turning points are also unstable. The instability of the latter is related to the possibility that pairs of complex conjugate eigenvalues cross the real axis in the κ plane. Zh. éksp. Teor. Fiz. 114, 1487–1499 (October 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Three fluid hydrodynamics of superfluid3He

TheA ₂-transition from theA ₁ to theA-phase is the only known transition that seperates a state with a broken relative symmetry from one in which both constituent symmetries are independently broken. Therefore a question of interest here is what the Goldstone mode of this transition is. Employing two different points of view, one for its rigor and the other because of its plausible physical picture, a three fluid hydrodynamics is derived and employed to show that, with a grain of salt, theA ₂-transition can be taken as marked by the onset of spin wave in a restricted geometry and by that of second sound generally. More quantitatively, the transition of the Goldstone modes takes place below theA ₂ transitional temperature when the Leggett frequency is approached and is caused by two competing effects, hybridization and dispersion. In a fourth sound geometry these effects should be experimentally well accessible.     

Asymmetric wave propagation in nonlinear systems

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schr?dinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wave packet transmission are presented which beautifully display the rectifying effect.     

Statistical mechanics of dilute mixtures of 3He in superfluid 4He

A statistical mechanical theory of the dilute mixtures of ³He and ⁴He is presented. It is shown that the ground state energy is proportional to the ³He density. The chemical potential expressed in terms of the sound velocity assumes the form which has been suggested phenomenologically. From the chemical potential, the effective ³He⁴He interaction and osmotic pressure are derived. The effective mass of ³He is also calculated as a function of potential parameters.     

Dissipative currents in superfluid 3He weak links

We calculate the current-pressure relation for pinholes connecting two volumes of bulk superfluid 3He-B. The theory of multiple Andreev reflections, adapted from superconducting weak links, leads to a nonlinear dependence of the dc current on pressure bias. In arrays of pinholes one has to take into account oscillations of the texture at the Josephson frequency. The associated radiation of spin waves from the junction leads to an additional dissipative current at small biases, in agreement with measurements.     

Nonlinear regimes in spin dynamics of superfluid 3He

We study an algebra of Poisson brackets of the Hamiltonian system defined by the nonlinear Leggett equations of spin dynamics in the A- and the B-phases of superfluid ³He. For the A-phase the Poisson algebra results in a special case of the equations of motion of a rigid body in ideal fluid; for the B-phase, in the absence of magnetic field, it allows for a reduction to a smaller Poisson algebra that provides exact solutions for the Leggett equations.