In this thesis, we present a mathematical study of three problems arising in the kinetic theory of quantum gases. In the first part, we consider a Boltzmann equation that is used to describe the time evolution of the ...

The discovery of high-temperature superconductors in 1986 represented a major experimental breakthrough (Nobel Prize 1987), but their theoretical explanation is still a subject of much debate. These materials have many ...

A Boltzmann equation, used to describe the Compton scattering in the non-relativistic limit is considered. A truncation of the very singular redistribution function is introduced and justified. The existence of weak solutions ...

The existence of global solutions for a system of differential equations is proved, and some of their properties are described. The system involves a kinetic equation for quantum particles. It is a simplified version of ...

High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows ...

We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903--931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time ...