16 citations · 69 across the 18 of their papers we have counts for
12 papers · 1 filter
Scattering and Pairing by Exchange Interactions
J. -B. Bru, W. de Siqueira Pedra, A. Ramer dos Santos
Quantum interactions exchanging different types of particles play a pivotal rôle in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspec…
From Short-Range to Mean-Field Models in Quantum Lattices
J. -B. Bru, W. de Siqueira Pedra, K. Rodrigues Alves
Realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range. However, the rigorous mathematical analysis of this type of model…
Large Deviations in Weakly Interacting Fermions -- Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians
N. J. B. Aza, J. -B. Bru, W. de Siqueira Pedra +1
We prove that the Gärtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the lim…
Classical Dynamics from Self-Consistency Equations in Quantum Mechanics -- Extended Version
J. -B. Bru, W. de Siqueira Pedra
During the last three decades, P. Bóna has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setti…
Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
J. -B. Bru, W. de Siqueira Pedra
We define a Banach space of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibri…
Bounds on the Pure Point Spectrum of Lattice Schrödinger Operators
Volker Bach, Walter de Siqueira Pedra, Saidakhmat Lakaev
In dimension , a variational principle for the size of the pure point spectrum of (discrete) Schrödinger operators on the hypercubic lattice $\mathbb{Z…
Universal Bounds for Large Determinants from Non-Commutative Hölder Inequalities in Fermionic Constructive Quantum Field Theory
J. -B. Bru, W. de Siqueira Pedra
Efficiently bounding large determinants is an essential step in non-relativistic fermionic constructive quantum field theory to prove the absolute convergence of the perturbation e…
Microscopic Conductivity of Lattice Fermions at Equilibrium - Part II: Interacting Particles
Jean-Bernard Bru, Walter de Siqueira Pedra
We apply Lieb-Robinson bounds for multi-commutators we recently derived to study the (possibly non-linear) response of interacting fermions at thermal equilibrium to perturbations…
Microscopic Foundations of Ohm and Joule's Laws - The Relevance of Thermodynamics
J. -B. Bru, W. de Siqueira Pedra
We give a brief historical account on microscopic explanations of electrical conduction. One aim of this short review is to show that Thermodynamics is fundamental to the theoretic…
Macroscopic Conductivity of Free Fermions in Disordered Media
J. -B. Bru, W. de Siqueira Pedra, C. Hertling
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…
Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles
J. -B. Bru, W. de Siqueira Pedra, C. Hertling
We consider free lattice fermions subjected to a static bounded potential and a time- and space-dependent electric field. For any bounded convex region $\mathcal{R}\subset \mathbb{…
Microscopic Foundations of the Meißner Effect - Thermodynamic Aspects
J. -B. Bru, W. de Siqueira Pedra
We analyze the Meißner effect from first principles of quantum mechanics. We show in particular the existence of superconducting states minimizing the magnetic free-energy of BCS-l…