In this document we discuss the long time behaviour for homogeneous Landau-Fermi-Dirac equation in hard potential case. Uniform estimates statistical moments and Sobolev regularity are presented used to prove exponential relaxation of non degenerate distributions Fermi-Dirac statistics. All these results valid rather general initial datum. An important feature is independence with respect quant...

We investigate low temperature (T ) properties of three classical quantum statistics models: (I) the Fermi-Dirac equation, (II) the Boltzman equation, and (III) the Bose-Einstein equation. It is widely assumed that each of these equations is valid for all T > 0. For each equation we prove that this assumption leads to erroneous predictions as T → 0. Our approach to correct these errors gives ne...

By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-de Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal-superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: (1) the electron and hole occupy different valleys of the band structure; (2) at normal...

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi-liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is, the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics...

On the basis of the Kadanoff-Baym (KB) version of the time-dependent Green’s function method a new ansatz for the approximation of a spectral function is offered. The ansatz possesses all the advantages of quasiparticle (QP) and extended quasiparticle (EQP) approximations and satisfies the KB-equation for a spectral function in the case of slightly non-equilibrium system when disturbances in sp...

In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate, or equivalently, by the hydrodynamic equations for the number density and the current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equat...

First, the Thomas-Fermi-Amaldi (TFA) equation was formulated with a newly derived condition to remove the singularities at the nuclei, which coincided with the molecular cusp condition. Next, the collocation method was applied to the TFA equation using the grid-based density functional theory. In this paper, the electron densities and the radial probabilities for specific atoms (He, Be, Ne, Mg,...