The interaction-induced orbital magnetic response of a nanoscale system, modeled by the persistent current in a ring geometry, is evaluated for a system which is a superconductor in the bulk. The interplay of the renormalized Coulomb and Fr{o}hlich i
nteractions is crucial. The diamagnetic response of the large superconductor may become paramagnetic when the finite-size-determined Thouless energy is larger than or on the order of the Debye energy.
The contributions of superconducting fluctuations to the specific heat of dirty superconductors are calculated, including quantum and classical corrections to the `usual leading Gaussian divergence. These additional terms modify the Ginzburg criterio
n, which is based on equating these fluctuation-generated contributions to the mean-field discontinuity in the specific heat, and set limits on its applicability for materials with a low transition temperature.
We calculate the contribution of superconducting fluctuations to the mesoscopic persistent current of an ensemble of rings, each made of a superconducting layer in contact with a normal one, in the Cooper limit. The superconducting transition tempera
ture of the bilayer decays very quickly with the increase of the relative width of the normal layer. In contrast, when the Thouless energy is larger than the temperature then the suppression of the persistent current with the increase of this relative width is much slower than that of the transition temperature. This effect is similar to that predicted for magnetic impurities, although the proximity effect considered here results in pair-weakening as opposed to pair-breaking.
We study the relaxation modes of an interface between a lyotropic lamellar phase and a gas or a simple liquid. The response is found to be qualitatively different from those of both simple liquids and single-component smectic-A liquid crystals. At lo
w rates it is governed by a non-inertial, diffusive mode whose decay rate increases quadratically with wavenumber, $|omega|=Aq^2$. The coefficient $A$ depends on the restoring forces of surface tension, compressibility and bending, while the dissipation is dominated by the so-called slip mechanism, i.e, relative motion of the two components of the phase parallel to the lamellae. This surface mode has a large penetration depth which, for sterically stabilised phases, is of order $(dq^2)^{-1}$, where $d$ is the microscopic lamellar spacing.
