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Equilibrium and Transport Properties of Quantum Many-Body Systems
(2019-10-30)
This thesis is a study of equilibrium and dynamical properties of macroscopic quantum many-body problems. An important part of the manuscript concerns the study of heat and charge transport properties of fermions on the ...
Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media
(J. Math. Pures Appl., 2019-01-22)
The growing need for smaller electronic components has recently sparked the interest in the breakdown of the classical conductivity theory near the atomic scale, at which quantum effects should dominate. In 2012, experimental ...
The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos
(The Astrophysical Journal, 2019-01-10)
We investigate the old problem of the fast relaxation of collisionless N-body systems that are collapsing or perturbed,
emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in ...
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 ...
Universal bounds for large determinants from non-commutative Hölder inequalities in fermionic constructive quantum field theory
(Mathematical Models and Methods in Applied Sciences (M3AS), 2017-08-02)
Efficiently bounding large determinants is an essential step in non-relativistic fermionic constructive quantum field theory to prove the absolute convergence of the perturbation expansion of correlation functions in terms ...