We present in this document some essential properties of solutions to the homogeneous Landau-Fermi-Dirac equation for moderately soft potentials. Uniform time estimates statistical moments, $L^{p}$-norm generation and Sobolev regularity are shown using a combination techniques that include recent developments concerning level set analysis spirit De Giorgi refined entropy-entropy dissipation fun...

We calculate corrections to the BCS gap equation caused by the interaction of electrons with the collective phase and amplitude modes in the superconducting state. This feedback reduces the BCS gap parameter, ∆, and leaves the critical temperature, Tc, unchanged. The feedback effect is proportional to (∆/EF ), where EF is the Fermi energy. This is a negligible correction for type-I superconduct...

We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This ...

Diffusive moment equations with an arbitrary number of moments are formally derived from the semiconductor Boltzmann equation employing a moment method and a Chapman-Enskog expansion. The moment equations are closed by employing a generalized Fermi-Dirac distribution function obtained from entropy maximization. The current densities allow for a drift-diffusion-type formulation or a “symmetrized...