### Recent Submissions

• #### Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model ﻿

(2020)
The aim of the current paper is to illustrate, in a simple example, our recent, very general, rigorous results on the dynamical properties of fermions and quantum-spin systems with long-range, or mean-field, interactions, ...
• #### Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media ﻿

(2020)
We contribute an extension of large-deviation results obtained in [N.J.B. Aza, J.-B. Bru, W. de Siqueira Pedra, A. Ratsimanetrimanana, J. Math. Pures Appl. 125 (2019) 209] on conductivity theory at atomic scale of free ...
• #### Weak* Hypertopologies with Application to Genericity of Convex Sets ﻿

(2022)
We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most well-studied and well-known ...
• #### Large Deviations in Weakly Interacting Fermions - Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians ﻿

(2021)
We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin ...
• #### Classical dynamics generated by long-range interactions for lattice fermions and quantum spins ﻿

(2021)
We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. The results obtained are far beyond previous ones and require the development of a mathematical ...
• #### Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model, ﻿

(2020)
The aim of the current paper is to illustrate, in a simple example, our recent, very general, rigorous results on the dynamical properties of fermions and quantum-spin systems with long-range, or meanfield, interactions, ...
• #### Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory ﻿

(2017)
We generalize to multi-commutators the usual Lieb–Robinson bounds for commutators. In the spirit of constructive QFT, this is done so as to allow the use of combinatorics of minimally connected graphs (tree expansions) in ...
• #### Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermion and Quantum Spins ﻿

(2021)
We study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which turns out to be equivalent to an intricate combination of classical and short-range quantum dynamics. ...
• #### 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 ...

(2013-07)
We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in ... • #### Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors ﻿ (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 ... • #### Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media ﻿ (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 ... • #### Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices ﻿ (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 ... • #### The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos ﻿ (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 ... • #### 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 ...
• #### Universal bounds for large determinants from non-commutative Hölder inequalities in fermionic constructive quantum field theory ﻿

(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 ...
• #### Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors ﻿

(2017-05-03)
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 ...