Quantum Mechanics
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A b-symplectic slice theorem
(2022-01-01)In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b -symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864–896, we ... -
Classical dynamics from self-consistency equations in quantum mechanics
Bru, J.-B.
; de Siqueira Pedra, W. (2022-05-09)
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 setting which is convenient to study the emergence ... -
Time Dynamics in Quantum Field Theory Systems
(2022-12-23)In this doctoral thesis, we develop and investigate new mathematical tools that are intended to allow for a rigorous description of non–perturbative quantum field theory (QFT) dynamics. Here, the term QFT is to be understood ... -
Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
(2022-04-28)We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on ... -
Extended State Space for Describing Renormalized Fock Spaces in QFT
(2022-06-04)In quantum field theory (QFT) models, it often seems natural to use, instead of wave functions from Fock space, wave functions that are not square-integrable and have prefactors involving divergent integrals (known as ... -
Entanglement of classical and quantum short-range dynamics in mean-field systems
Bru, J. B.; de Siqueira Pedra, W. (2021-11-01)
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 Bose-Hubbard model on a finite graph
(2021-08-01)The Kubo-Martin-Schwinger (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
(2021-10-14)In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well ... -
Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model
Bru, J.-B.; de Siqueira Pedra, W. (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, ... -
Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media
Bru, J.-B.; de Siqueira Pedra, W.; Ratsimanetrimanana, A. (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 ... -
Weak* Hypertopologies with Application to Genericity of Convex Sets
Bru, J.-B.; de Siqueira Pedra, W. (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 well-studied and well-known ... -
Large Deviations in Weakly Interacting Fermions - Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians
Aza, N. J. B.; Bru, J.-B.; de Siqueira Pedra, W.; Müssnich, L. C. P. A. M. (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 ... -
Classical dynamics generated by long-range interactions for lattice fermions and quantum spins
Bru, J.-B.; de Siqueira Pedra, W. (2021)
We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. The results obtained are far beyond previous ones and require the development of a mathematical ... -
Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model,
Bru, J.-B.; de Siqueira Pedra, W. (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, ... -
Lieb–Robinson Bounds for Multi–Commutators and Applications to Response Theory
Bru, J.-B.; de Siqueira Pedra, W. (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 ... -
Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermion and Quantum Spins
Bru, J.-B.; de Siqueira Pedra, W. (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. ... -
Equilibrium and Transport Properties of Quantum Many-Body Systems
(2019-10-30)This thesis is a study of equilibrium and dynamical properties of macroscopic quantum many-body problems. An important part of the manuscript concerns the study of heat and charge transport properties of fermions on the ... -
Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
Bru, J.-B.; de Siqueira Pedra, W. (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 ... -
Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors
Bru, J.-B.; de Siqueira Pedra, W.; Delgado de Pasquale, A. (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 ... -
Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media
Aza, N.J.B.; Bru, J.-B.; de Siqueira Pedra, W.; Ratsimanetrimanana, A. (2019-01-22)
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 ...
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