Narrow Results

The thermodynamic impact of the Coulomb repulsion on s-wave superconductors is analyzed via a rigorous study of equilibrium and ground states of the strong coupling BCS-Hubbard Hamiltonian. We show that the one-site electron repulsion can favor superconductivity at fixed chemical potential by increasing the critical temperature and/or the Cooper pair condensate density. If the one-site repulsion is not too large, a first or a second order superconducting phase transition can appear at low temperatures. The Meißner effect is shown to be rather generic but coexistence of superconducting and ferromagnetic phases is also shown to be feasible, for instance, near half-filling and at strong repulsion. Our proof of a superconductor-Mott insulator phase transition implies a rigorous explanation of the necessity of doping insulators to create superconductors. These mathematical results are consequences of "quantum large deviation" arguments combined with an adaptation of the proof of Størmer's theorem [1] to even states on the CAR algebra.

The problem of incident plane waves at the interface of micropolar thermoelastic half-space with voids and micropolar elastic half-space with voids has been attempted. The amplitude and energy ratios of various reflected and refracted waves for the incident $P$- and $S$-waves are obtained with the help of appropriate boundary conditions at the interface. The effect of linear thermal expansion and microinertia on the amplitude and energy ratios due to the incident $P$- and $S$-waves are discussed. Numerically and analytically, these amplitude and energy ratios are computed to show the effect of linear thermal expansion and microinertia. It is observed that the effect of linear thermal expansion is less for incident $S$-wave and the effect of microinertia is less for incident $P$-wave.