16 citations · 69 across the 18 of their papers we have counts for
18 papers
Nonlinear Thermodynamic Formalism: Mean-field Phase Transitions, Large Deviations and Bogoliubov's Variational Principle
Jean-Bernard Bru, Walter de Siqueira Pedra, Artur O. Lopes
Let , be the shift acting on , the set of -invariant probabilities. Given a Hölder potential and a continuous funct…
Minimum-entropy constraints on galactic potentials
Leandro Beraldo e Silva, Monica Valluri, Eugene Vasiliev +3
A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increas…
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…
Threshold effects of the two-particle Schrödinger operators on lattices
Saidakhmat N. Lakaev, Volker Bach, W. de Siqueira Pedra
We consider a wide class of the two-particle Schrödinger operators with a fixed two-particle quasi-momentum in the -dimensional torus $\mathbb{…
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…
The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos
Leandro Beraldo e Silva, Walter de Siqueira Pedra, Monica Valluri +2
We investigate the old problem of the fast relaxation of collisionless -body systems which are collapsing or perturbed, emphasizing the importance of (non-collisional) discreten…
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…
The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation
Leandro Beraldo e Silva, Walter de Siqueira Pedra, Laerte Sodré +2
The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting…
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{…
Remarks on the -regularization of Non-convex and Non-semi-continuous Functions on Topological Vector Spaces
J. -B. Bru, W. de Siqueira Pedra
We show that the minimization problem of any non-convex and non-lower semi-continuous function on a compact convex subset of a locally convex real topological vector space can be s…
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…