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H. Bergeron

Publications and source records attributed to H. Bergeron.

13 recordsLinked to original sources
arXiv2018

The need for an integrative thinking to fight against emerging infectious diseases

We present here the proceedings of the 5th seminar on emerging infectious diseases (EIDs), held in Paris on March 22nd, 2016, with seven priority proposals that can be outlined as follows:$\bullet$Encourage research on the prediction, screening and early detection of new risks of infection$\bullet$Develop research and surveillance concerning transmission of pathogens between animals and humans, with their reinforcement in particular in intertropical areas (`hot-spots') thanks to public support$\bullet$Pursue aid development and support in these areas of prevention and training for local health personnel, and to foster risk awareness in the population$\bullet$Ensure adapted patient care in order to promote adherence to treatment and to epidemic propagation reduction measures$\bullet$Develop greater sensitization and training among politicians and healthcare providers, in order to better prepare them to respond to new types of crises$\bullet$Modify the logic of governance, drawing from all available modes of communication and incorporating new information-sharing tools$\bullet$Develop economic research on the fight against EIDs, taking into account specific driving factors in order to create a balance between preventive and treatment approaches.

q-bio.OT↗
arXiv2018

Integrable Toda system as a quantum approximation to the anisotropy of Mixmaster

We present a regularisation approach to the study of the quantum dynamics of the Mixmaster universe which allows to approximate the anisotropy potential with the explicitly integrable periodic 3-particle Toda system. This approach is based on a covariant Weyl-Heisenberg integral quantization. Such a procedure naturally amplifies the dynamical role of the underlying Toda system by smoothing out the three canyons of the anisotropy potential. Since the respective eigenfunctions can be explicitly constructed, our finding paves the way to a novel perturbative approach to the quantum Mixmaster dynamics.

gr-qc↗
arXiv2014

Entropies of deformed binomial distributions

Asymptotic behavior (with respect to the number of trials) of symmetric generalizations of binomial distributions and their related entropies are studied through three examples. The first one derives from the q-exponential as a generating function. The second one involves the modified Abel polynomials, and the third one involves Hermite polynomials. The former and the latter have extensive Boltzmann-Gibbs whereas the second one (Abel) has extensive Renyi entropy. A probabilistic model is presented for this exceptional case.

cond-mat.stat-mech↗
arXiv2013

Symmetric generalized binomial distributions

In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in this article another generalization (always associated with a sequence of positive numbers) that preserves the symmetry {\it win-loss}. This approach is also based on generating functions and presents constraints of non-negativeness, similar to those encountered in our previous articles.

math-ph↗
arXiv2012

Generating functions for generalized binomial distributions

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties: the constraints of nonnegativeness are automatically fulfilled, a complete characterization in terms of generating functions is given and a large number of analytical examples becomes available.

math-ph↗
arXiv2012

Sticking coefficient of hydrogen and deuterium on silicates under interstellar conditions

Sticking of H and D atoms on interstellar dust grains is the first step in molecular hydrogen formation, which is a key reaction in the InterStellar Medium (ISM). After studying the sticking coefficients of H2 and D2 molecules on amorphous silicate surfaces experimentally and theoretically, we extrapolate the results to the sticking coefficient of atoms and propose a formulae that gives the sticking coefficients of H and D on both silicates and icy dust grains. In our experiments, we used the King and Wells method for measuring the sticking coefficients of H2 and D2 molecules on a silicate surface held at 10 K. It consists of measuring with a QMS (quadrupole mass spectrometer) the signals of H2 and D2 molecules reflected by the surface during the exposure of the sample to the molecular beam at a temperature ranging from 20 K to 340 K. We tested the efficiency of a physical model, developed previously for sticking on water-ice surfaces. We applied this model to our experimental results for the sticking coefficients of H2 and D2 molecules on a silicate surface and estimated the sticking coefficient of atoms by a single measurement of atomic recombination and propose an extrapolation. Sticking of H, D, HD, H2, and D2 on silicates grains behaves the same as on icy dust grains. The sticking decreases with the gas temperature, and is dependent on the mass of the impactor. The sticking coefficient for both surfaces and impactors can be modeled by an analytical formulae S(T), which describes both the experiments and the thermal distribution expected in an astrophysical context. The parameters S0 and T0 are summarized in a table. Previous estimates for the sticking coefficient of H atoms are close to the new estimation; however, we find that, when isotopic effects are taken into account, the sticking coefficient variations can be as much as a factor of 2 at T=100 K.

astro-ph.IM↗
arXiv2012

New SUSYQM coherent states for Poschl-Teller potentials: a detailed mathematical analysis

In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for Pöschl-Teller potentials. These states are built from a supersymmetric quantum mechanics approach and the parameters of these "coherent" states are points in the classical phase space. In this article we develop all the mathematical aspects that have been left apart in the previous article (proof of the resolution of unity, detailed calculations of quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self- adjointness or self-adjoint extensions). Some additional questions as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Pöschl-Teller potentials.

math-ph↗
arXiv2011

About Statistical Questions Involved in the Data Analysis of the OPERA Experiment

The authors of the OPERA experiment [arXiv:1109.4897] claim that "the measurement indicates an early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum". In this note we analyze the statistical aspects of the experimental results presented in [arXiv:1109.4897], assuming that no hidden experimental bias exists. Due to statistical constraints, we show (through two different methods) that the experimental data presented in [arXiv:1109.4897] do not permit to conclude unambiguously with the existence of a superluminal behavior of neutrinos. The problem lies essentially in the interpretation of the data and not in their veracity.

hep-ph↗
arXiv2010

Gas temperature dependent sticking of hydrogen on cold amorphous water ice surfaces of interstellar interest

Using the King & Wells method, we present experimental data on the dependence of the sticking of molecular hydrogen and deuterium on the beam temperature onto non- porous amorphous solid water (ASW) ice surfaces of interstellar interest. A statistical model that explains the isotopic effect and the beam temperature behavior of our data is proposed. This model gives an understanding of the discrepancy between all known experimental results on the sticking of molecular hydrogen. Moreover it is able to fit the theoretical results of V. Buch et al. [Astrophys. J. (1991), 379, 647] on atomic hydrogen and deuterium. For astrophysical applications, an analytical formula for the sticking coefficients of H, D, H2, D2 and HD in the case of a gas phase at thermal equilibrium is also provided at the end of the article.

physics.chem-ph↗
arXiv2010

Semi-classical behavior of Pöschl-Teller coherent states

We present a construction of semi-classical states for Pöschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They minimize a special uncertainty relation. Like standard coherent states they resolve the identity with a uniform measure. They permit to establish the correspondence (quantization) between classical and quantum quantities. Finally, their time evolution is localized on the classical phase space trajectory.

quant-ph↗
arXiv2003

New derivation of quantum equations from classical stochastic arguments

In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This procedure was based on a Koopman-von Neumann approach where classical equations are reformulated into a quantumlike form. In this article, we develop a different derivation of quantum equations, based on purely classical stochastic arguments, taking some elements from the Bohm-Fenyes-Nelson approach. This study starts from a remark noticed by different authors [M. Born, Physics in My Generation (Pergamon Press, London, 1956); E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime (Reidel, Dordrecht, 1986)], suggesting that physical continuous observables are stochastic by nature. Following this idea, we study how intrinsic stochastic properties can be introduced into the framework of classical mechanics. Then we analyze how the quantum theory can emerge from this modified classical framework. This approach allows us to show that the transition from classical to quantum formalism (for a spinless particle) does not require real postulates, but rather soft generalizations.

quant-ph↗
arXiv2001

From Classical to Quantum Mechanics: "How to translate physical ideas into mathematical language"

In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint operators and so on) - Quantum Mechanics properly that specifies the Hilbert space, the Heisenberg rule, the free Hamiltonian... We show that General Quantum Axiomatics (up to a supplementary "axiom of classicity") can be used as a non-standard mathematical ground to formulate all the ideas and equations of ordinary Classical Statistical Mechanics. So the question of a "true quantization" with "h" must be seen as an independent problem not directly related with quantum formalism. Moreover, this non-standard formulation of Classical Mechanics exhibits a new kind of operation with no classical counterpart: this operation is related to the "quantization process", and we show why quantization physically depends on group theory (Galileo group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows to map Classical Mechanics into Quantum Mechanics, giving all operators of Quantum Mechanics and Schrodinger equation. Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We find also that this approach gives a natural semi-classical formalism: some exact quantum results are obtained only using classical-like formula. So this procedure has the nice property of enlightening in a more comprehensible way both logical and analytical connection between classical and quantum pictures.

quant-ph↗