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Classical dynamics from self-consistency equations in quantum mechanics
(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 ...
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 well-studied and
well-known ...
Entanglement of classical and quantum short-range dynamics in mean-field systems
(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 ...
Classical dynamics generated by long-range interactions for lattice fermions and quantum spins
(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 ...
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. ...
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 ...
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 ...
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, ...
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, ...
Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media
(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 ...