Now showing items 14-33 of 35

• #### Heat production of noninteracting fermions subjected to electric fields ﻿

(2014-07-21)
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 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 ...
• #### 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 ...
• #### Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction ﻿

(2016-01-01)
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}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 ...
• #### Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory ﻿

(2016-01-01)
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 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 ...
• #### Macroscopic conductivity of free fermions in disordered media ﻿

(2014-12-31)
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 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, ...
• #### 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, ...
• #### 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 ...
• #### Microscopic conductivity of lattice fermions at equilibrium. I. Non-interacting particles ﻿

(2015-12-31)
We consider free lattice fermions subjected to a static bounded potential and a timeand space-dependent 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 ﻿

(2016-01-01)
We apply Liebâ€“Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Liebâ€“Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) ...
• #### Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles ﻿

(2015-12-31)
We apply Lieb–Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) ...
• #### Non-cooperative Equilibria of Fermi Systems With Long Range Interactions ﻿

(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 ...
• #### 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 ...
• #### 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. ...
• #### 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 ...
• #### 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 ...