An expression for the static structure factor,g⁺⁻ (r), of electrons at a distancer from an infinitely heavy positively charged particle in a one component quantum rare plasma has been obtained in linear response theory using an appropriate quantum dielectric function of the rare plasma. The expression is a complicated function of the electron plasma frequency, Debye screening length andr, but reduces to that of classical plasma when quantum corrections are neglected. Forr<r_s (2r_s being the mean distance between two electrons), the temperature dependentg⁺⁻ (r) has larger values in quantum case in comparison to that in classical situation and keeps increasing with decrease inr, more so at low temperatures when de-Broglie wavelength becomes larger and a considerable fraction ofr_s.

The full wavevector and frequency dependent complex dielectric function for two component classical and quantum rare hot plasmas have been derived. The real part of dielectric function is obtained in the form of a series. Difference between quantum and classical real and imaginary parts of dielectric function have been brought out by making explicit calculations. The quantum nature of the plasma brings about significant changes in both parts depending upon the magnitude of quantum parameter,R (= 8.93(λ_th)/λ).

Expressions for the dynamic structure factors for both two component classical and quantum plasma have been evaluated for different values of the mass of the positive componentm₊, temperature T₊ and wavevector k. It is found that the plasma exhibits well defined collective modes for certain values of ¦k¦ accompanied by varying disorder which depends upon the values of m₊ as well as on ¦k¦ and T₊. For the quantum case the collective modes are less well defined as compared to the corresponding classical case, thus proving that quantum nature introduces inherent disorder in the system. But for both the cases, increase in temperature destroys collective modes. Another feature is the appearance of a hump near Ω = 0 which becomes smaller and vanishes as the quantum parameter is decreased.

Instability of plasma modes in the presence of constant electric field has also been worked out for the quantum case.

Superconducting behavior of the fragile, pure, sub-milli-Kelvin temperature superconductor rhodium has been studied. Rhodium, a paramagnetic transition element, having a free electron density, more than an order of magnitude larger (6.5×10$^{23}$ cm$^{−3}$) than a metallic monovalent superconductor, exhibits superconductivity at an extremely low temperature of a few hundred micro-Kelvin (10$^{−6}$ K), at ambient pressure. Rhodium exhibits traditional BCS superconductivity brought about by the residual electron-phonon interaction and showsthe characteristics of Type-I superconductivity. In this work, we have studied the effect of electron–phonon, electron–electron and electron–paramagnon interactions in rhodium. Further, we have evaluated the various characteristic parameters associated with rhodium. Finally, we conclude that rhodium is explained totally by the Bardeen–Cooper–Schrieffer (BCS) theory which corresponds fundamentally to the instantaneous nature of electron–phonon interaction along with the instantaneous electron–Coulomb interaction and instantaneous electron–spin interaction.