Quantum Mechanics
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Langevin equation in complex media and anomalous diffusion
(J. Math. Anal. Appl., 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 ... -
Logarithmic connections on principal bundles over a Riemann surface
(Physics of Particles and Nuclei, 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, ... -
On a system of equations for the normal fluid - condensate interaction in a Bose gas
(Springer Briefs in Math. Phys., 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 ... -
On the merits of sparse surrogates for global sensitivity analysis of multi-scale nonlinear problems: Application to turbulence and fire-spotting model in wildland fire simulators
(J. Math. Anal. Appl., 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. ... -
The M-Wright function as a generalization of the Gaussian density for fractional diffusion processes
(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
(Memoirs of the AMS, 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 ... -
The role of the environment in front propagation
(Ann. Phys. (Berl.), 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 ... -
Wildfire propagation modelling
(J. Math. Pures Appl., 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 ... -
Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers
(Commun. Math. Phys., 2018-01-24)We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903--931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time ... -
Short note on the emergence of fractional kinetics
(The Astrophysical Journal, 2019-01-10)We investigate the old problem of the fast relaxation of collisionless N-body systems that are collapsing or perturbed, emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in ... -
The emergence of self-organization in complex systems-Preface
(2018-12-19)In this thesis, we present a mathematical study of three problems arising in the kinetic theory of quantum gases. In the first part, we consider a Boltzmann equation that is used to describe the time evolution of the ... -
Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency
(2018-08-15)A Boltzmann equation, used to describe the Compton scattering in the non-relativistic limit is considered. A truncation of the very singular redistribution function is introduced and justified. The existence of weak solutions ... -
Fractional relaxation with time-varying coefficient
(2018-03-27)The existence of global solutions for a system of differential equations is proved, and some of their properties are described. The system involves a kinetic equation for quantum particles. It is a simplified version of ... -
Velocity and energy distributions in microcanonical ensembles of hard spheres
(2018-03-21)High-temperature superconductors have different properties than conventional superconductors, one of these important properties is non-isotropic symmetry of the order parameter. In this work we present a model that shows ... -
Heat production of noninteracting fermions subjected to electric fields
(Mathematical Models and Methods in Applied Sciences (M3AS), 2017-08-02)Efficiently bounding large determinants is an essential step in non-relativistic fermionic constructive quantum field theory to prove the absolute convergence of the perturbation expansion of correlation functions in terms ... -
Front propagation in anomalous diffusive media governed by time-fractional diffusion
(2017-05-03)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 ... -
Turbulence and fire-spotting effects into wild-land fire simulators
(2016-07-22)We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results ... -
Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs
(Memoirs of the American Mathematical Society, 2016-01-01)We study a non-autonomous, non-linear 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 ... -
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(Journal of Statistical Mechanics: Theory and Experiment, 2015-12-31)Taking into account microscopic properties of most usual high-Tc superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the ... -
Neron models of intermediate Jacobians associated to moduli spaces
(Journal of Mathematical Physics, 2015-12-31)We consider free lattice fermions subjected to a static bounded potential and a timeand space-dependent electric field. For any bounded convex region R ⊂ ℠(d (d ≥ 1) of space, electric fields ε within R drive currents. ...
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