T
+34 946 567 842
F
+34 946 567 842
E
jbru@bcamath.org
Information of interest
 Orcid: 0000000191599407
Other links
Personal website at IkerbasqueMy first researches have been related to mathematical studies of phase transitions associated with Bose gases. Since then, the bulk of my research has considerably widened and covers a scope from mathematical analyzes of the quantum many body problem to operator algebras, stochastic processes, differential equations, game theory, convex and functional analysis. I am particularly interested in the mathematical foundations of statistical mechanics with applications in the study of phase transitions and transport properties.

Classical dynamics from selfconsistency equations in quantum mechanics
(20220509)During the last three decades, P. Bóna has developed a nonlinear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence ...

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 ...

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 ...

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. ...

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 ...

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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

Universal bounds for large determinants from noncommutative Hölder inequalities in fermionic constructive quantum field theory
(20170802)Efficiently bounding large determinants is an essential step in nonrelativistic fermionic constructive quantum field theory to prove the absolute convergence of the perturbation expansion of correlation functions in terms ...

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 ...

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 ...

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) ...

Diagonalizing quadratic bosonic operators by nonautonomous flow equations volker bach
(20160101)We study a nonautonomous, nonlinear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics ...

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) ...

Universal Bounds for Large Determinants from Non–Commutative Ho ̈lder Inequalities in Fermionic Constructive Quantum Field Theory
(20160101)Efficiently bounding large determinants is an essential step in non–relati vistic fermionic constructive quantum field theory, because, together with the summability of the interaction and the covariance, it implies the ...

Characterization of the QuasiStationary State of an Impurity Driven by Monochromatic Light II: Microscopic Foundations
(20151231)From quantum mechanical first principles only, we rigorously study the timeevolution of a Nlevel atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at ...

DWave pairing driven by bipolaric modes related to giant electronphonon anomalies in highTc superconductors
(20151231)Taking into account microscopic properties of most usual highTc superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on 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. ...

ACConductivity Measure from Heat Production of Free Fermions in Disordered Media
(20151231)We extend (Bru et al. in J Math Phys 56:051901151, 2015) in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric ...

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) ...

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 ...

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 ...

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 ...

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 ...