Quantum Mechanics
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Entanglement of classical and quantum shortrange dynamics in meanfield systems
(20211101)The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity ... 
High temperature convergence of the KMS boundary conditions: The BoseHubbard model on a finite graph
(20210801)The KuboMartinSchwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and ... 
Another Proof of Born's Rule on Arbitrary Cauchy Surfaces
(20211014)In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski spacetime assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well ... 
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, ... 
Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media
(2020)We contribute an extension of largedeviation 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 wellstudied and wellknown ... 
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 ... 
Classical dynamics generated by longrange interactions for lattice fermions and quantum spins
(2021)We study the macroscopic dynamical properties of fermion and quantumspin systems with longrange, or meanfield, interactions. The results obtained are far beyond previous ones and require the development of a mathematical ... 
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, ... 
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 ... 
Quantum Dynamics Generated by LongRange Interactions for Lattice Fermion and Quantum Spins
(2021)We study the macroscopic dynamics of fermion and quantumspin systems with longrange, or meanfield, interactions, which turns out to be equivalent to an intricate combination of classical and shortrange quantum dynamics. ... 
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 ... 
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 ... 
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 ... 
Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media
(20190122)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 Complextime Determinantal and Pfaffian\ Correlation Functionals in Lattices
(20180124)We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903931, 2016) for manybody localization of quasifree fermions, by considering the high dimensional case and complextime ... 
The Discretenessdriven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, Ndependence, and the Role of Chaos
(20190110)We investigate the old problem of the fast relaxation of collisionless Nbody systems that are collapsing or perturbed, emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in ... 
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 ... 
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 ... 
On a system of equations for the normal fluid  condensate interaction in a Bose gas
(20180327)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 ...