The transverse-spin modes in clusters of He-3 are considered. These excitations correspond to a gapless Goldstone mode which comes along due to the broken symmetry in the spin space, and can exhibit themselves in polarized He-3. These modes can be interpreted as weakly damped fluctuations of the transverse spin components, which propagate through He-3. The dispersion law of such spin waves is calculated by means of a semiclassical variational method and compared with the results obtained on the basis of the Fermi-liquid theory. The finite sizes of the clusters lead to quantization of the spectra and result in a series of excited states. The number of long-living excited states is strongly affected by the Landau damping. The orthogonality relations and energy-weighted sum rule are formulated. The collective spin modes for l=0 and several cluster sizes are computed.

We consider dimerization of He-3 in a dilute solution of He-3 in superfluid He-4 filling straight narrow channels that can be found in nanoscale porous media. Dimer formation is facilitated by the restricted geometry and occurs despite the fact that in bulk fluid the interparticle interaction is too weak to lead to a bound state. Dimerization results in the effective "bosonization" of the system: a Bose quantum fluid of (He-3), arises in place of the He-3 Fermi component. At high temperatures, when the He-3 impurity quasiparticles form a Maxwell-Boltzmann gas, a drastic change in the thermodynamics occurs due to the presence of dimers. The specific heat and magnetic susceptibility of the He-3 component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized He-3 component. We show that the binding energy-which depends on the channel width-is expected to be sufficiently high to make experimental observation feasible. The presence of (He-3), dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid He-4, due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single He-3 polymer will form over the entire length of the channel.

We consider dimerization of 3 He in a dilute solution of 3 He in superfluid 4 He filling narrow channels of a kind typically found in nanoscale porous media. Dimer formation is facilitated by the one dimensional geometry and occurs despite the fact that the interparticle interaction is too weak to lead to a bound state in bulk fluid. At sufficiently low temperatures, dimerization results in the effective "bosonization" of the system: a Bose quantum fluid of (3 He )2 arises in place of the 3 He Fermi component. At sufficiently high temperatures, for which the 3 He impurity quasiparticles form a Maxwell–Boltzmann gas, the thermodynamics is significantly affected by the presence of dimers. In particular, the specific heat and magnetic susceptibility of the 3 He component show a marked deviation from behaviour expected if dimers were absent. Solution of the Schrödinger equation for a smooth cylindrical pore indicates that the binding energy in straight nanoscale channels ought to be of sufficiently high magnitude to make experimental observation feasible. The presence of (3 He )2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4 He , due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single 3 He polymer will form over the entire length of the channel.

The thermodynamic stability of a trapped Bose gas with a two-component condensate, e.g., a gas of atoms in two distinct hyperfine states or a binary gaseous mixture, is considered on the basis of modified Gross-Pitaevskii equations. Under certain conditions the system becomes unstable with respect to stratification, i.e., to spatial separation between the two condensates. One condensate assumes a donutlike spatial distribution, while the other retains a centered distribution. Possible applications of the theory to recent experimental data on two overlapping condensates in Rb-87 are discussed.

Inelastic neutron scattering with the thermal fluctuations of density, magnetization, and entropy in spinpolarized3He systems (like liquid3He↓ and3He↓−4He dilute mixtures) is considered. Under certain conditions the scattering cross section is no longer described in terms of the density-density structure factor only, as prescribed by the conventional theory, but does include a large number of additional correlation functions. It is shown that the transverse spin modes can cause a drastic enhancement (several orders of magnitude!) in the small-angle scattering probability. The effects in question are not small at all and seem to be quite observable in the wake of the recent experiments on neutron scattering in3He fluids carried out by the Grenoble group.

3He atoms dissolved in super fluid4He may form aimers (3He)2 in twodimensional (2D) geometries. We study dimer formation in films of dilute3He-4He mixture. After designing a schematic3He-4He interaction potential we calculate the dimer binding energy for various substrates. It is shown that3He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.

It is shown that even a small amount of impurities can drastically affect the properties of charge carriers in superfluid4He. Under certain conditions the effective interaction between the carrier and foreign atom turns out to be attractive at large distances. This may result in a localization of the impurity on the electric charge in superfluid4He. The attraction causes a significant increase in the concentration of foreign atoms near the carrier (the impurity cloud) and produces around the charge a macroscopic region of radius 50–70 Å rich with the impurity component. 2D bound states of an electron or ion near the free surface of liquid4He and a3He surface impurity are considered. This effect can strongly influence the motion of the charge carriers inxy-plane, which can be studied in experiments on the mobility. Photoelectric absorption of radiation due to the decay of the bound state as well as tunnelling ionization in a static electric field are discussed. An extra scattering channel due to the interaction between an impurity and the hydrodynamic backflow around the moving “snowball” or “bubble” is described. Within the velocity range 1m/s−60m/s this scattering process becomes predomonant and determines the mobility of charged particles in superfluid4He.