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In the last decade, new techniques for producing impure superfluids with unique properties have been developed. This new class of systems includes superfluid helium confined to aerogel, HeII with different impurities, superfluids in Vycor glasses, and watergel. These systems exhibit very unusual properties including unexpected acoustic features. We discuss the sound properties of these systems and show that sound phenomena in impure superfluids are modified from those in pure superfluids.

We calculate the coupling between temperature and pressure oscillations for impure superfluids and show that this coupling increases significantly. This leads to the existence in impure superfluids of such unusual sound phenomena as slow "pressure" waves and fast "temperature" waves. This also decreases the threshold values for nonlinear processes as compared to pure superfluids. Sound conversion, which has been observed in pure superfluids only by high intensity waves should be observed at moderate sound amplitude in impure superfluids. Cerenkov emission of second sound by first sound (which has never been observed in superfluids) could be observed in impure superfluids. Even the nature of the sound modes in impure superfluids turns out to be changed. We have also derived for the first time the nonlinear hydrodynamic equations for superfluid helium in aerogel.

A numerical investigation for the stability of the incompressible slip flow of normal quantum fluids (above the critical phase transition temperature) inside a microslab where surface acoustic waves propagate along the walls is presented. Governing equations and associated slip velocity and wavy interface boundary conditions for the flow of normal fluids confined between elastic wavy interfaces are obtained. The numerical approach is an extension (with a complex matrix pre-conditioning) of the spectral method. We found that the critical Reynolds number (Re_cr or the critical velocity) decreases significantly once the slip velocity and wavy interface effects are present and the latter is dominated (Re_cr mainly depends on the wavy interfaces).

Although BCS pairs of fermions are known to obey neither Bose–Einstein (BE) commutation relations nor BE statistics, we show how Cooper pairs (CPs), whether the simple original ones or the CPs recently generalized in a many-body Bethe–Salpeter approach, being clearly distinct from BCS pairs at least obey BE statistics. Hence, contrary to widespread popular belief, CPs can undergo BE condensation to account for superconductivity if charged, as well as for neutral-atom fermion superfluidity where CPs, but uncharged, are also expected to form.

We obtain the possible transport in an annulus filled with solid helium of which parts are of supersolidity near the interface. Our transport results qualitatively resemble those recently reported measurements.

We present fundamental constraints required for a consistent linear response theory of fermionic superfluids and address temperatures both above and below the transition temperature T_c. We emphasize two independent constraints, one associated with gauge invariance (and the related Ward identity) and another associated with the compressibility sum rule, both of which are satisfied in strict BCS theory. However, we point out that it is the rare many body theory which satisfies both of these. Indeed, well studied quantum Hall systems and random-phase approximations to the electron gas are found to have difficulties with meeting these constraints. We summarize two distinct theoretical approaches which are, however, demonstrably compatible with gauge invariance and the compressibility sum rule. The first of these involves an extension of BCS theory to a mean field description of the BCS-Bose Einstein condensation crossover. The second is the simplest Nozieres Schmitt–Rink (NSR) treatment of pairing correlations in the normal state. As a point of comparison we focus on the compressibility κ of each and contrast the predictions above T_c. We note here that despite the compliance with sum rules, this NSR based scheme leads to an unphysical divergence in κ at the transition. Because of the delicacy of the various consistency requirements, the results of this paper suggest that avoiding this divergence may repair one problem while at the same time introducing others.