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Measure-valued weak solutions to some kinetic equations with singular kernels for quantum particles
(2018-12-19)
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 ...
Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors
(Ann. Phys. (Berl.), 2018-12-10)
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 ...
On a Boltzmann equation for Compton scattering, from non relativistic electrons at low density.
(2018-08-15)
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 ...
On a system of equations for the normal fluid - condensate interaction in a Bose gas
(2018-03-27)
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 ...
Existence of “$d$-wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors
(2018-03-21)
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 ...
Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices
(Commun. Math. Phys., 2018-01-24)
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 ...