Browsing Quantum Mechanics by Title
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Equilibrium and Transport Properties of Quantum ManyBody Systems
(20191030)This thesis is a study of equilibrium and dynamical properties of macroscopic quantum manybody problems. An important part of the manuscript concerns the study of heat and charge transport properties of fermions on the ... 
Existence of “$d$wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors
(20180321)Hightemperature superconductors have different properties than conventional superconductors, one of these important properties is nonisotropic symmetry of the order parameter. In this work we present a model that shows ... 
From the 2nd Law of Thermodynamics to AC–Conductivity Measures of Interacting Fermions in Disordered Media
(20150520)We study the dynamics of interacting lattice fermions with random hopping amplitudes and random static potentials, in presence of timedependent electromagnetic fields. The interparticle interaction is shortrange and ... 
Geometric inequalities from phase space translations
(20160722)We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results ... 
Heat production of noninteracting fermions subjected to electric fields
(20140721)Electric resistance in conducting media is related to heat (or entropy) production in the presence of electric fields. In this paper, by using Araki's relative entropy for states, we mathematically define and analyze the ... 
Isotropic BipolaronFermionExchange Theory and Unconventional Pairing in Cuprate Superconductors
(20170503)The discovery of hightemperature 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 ... 
Isotropic BipolaronFermionExchange Theory and Unconventional Pairing in Cuprate Superconductors
(20181210)The discovery of hightemperature 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 ... 
Kinetic energy estimates for the accuracy of the timedependent HartreeFock approximation with Coulomb interaction
(20160101)We study the time evolution of a system of $N$ spinless fermions in $\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation ... 
Large Deviations in Weakly Interacting Fermions  Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians
(2021)We prove that the G\"{a}rtnerEllis 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 ... 
Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory
(20160101)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 expan sions) ... 
Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory
(2017)We generalize to multicommutators 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 ... 
Macroscopic conductivity of free fermions in disordered media
(20141231)We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic ... 
Macroscopic Dynamics of the StrongCoupling BCSHubbard 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 quantumspin systems with longrange, or meanfield, interactions, ... 
Macroscopic Dynamics of the StrongCoupling BCSHubbard 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 quantumspin systems with longrange, or meanfield, interactions, ... 
Measurevalued weak solutions to some kinetic equations with singular kernels for quantum particles
(20181219)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 ... 
Microscopic conductivity of lattice fermions at equilibrium. I. Noninteracting particles
(20151231)We consider free lattice fermions subjected to a static bounded potential and a timeand spacedependent electric field. For any bounded convex region R âŠ‚ â„ (d (d â‰¥ 1) of space, electric fields Îµ within R drive currents. ... 
Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles
(20160101)We apply Liebâ€“Robinson bounds for multicommutators we recently derived (Bru and de Siqueira Pedra, Liebâ€“Robinson bounds for multicommutators and applications to response theory, 2015) to study the (possibly nonlinear) ... 
Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles
(20151231)We apply Lieb–Robinson bounds for multicommutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multicommutators and applications to response theory, 2015) to study the (possibly nonlinear) ... 
Noncooperative Equilibria of Fermi Systems With Long Range Interactions
(201307)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 ... 
On a Boltzmann equation for Compton scattering, from non relativistic electrons at low density.
(20180815)A Boltzmann equation, used to describe the Compton scattering in the nonrelativistic limit is considered. A truncation of the very singular redistribution function is introduced and justified. The existence of weak solutions ...