Séminaire: Problèmes Spectraux en Physique Mathématique

Année 2018-2019

Les séminaires auront lieu à l'Institut Henri Poincaré.
Le séminaire est financé par le GDR "Dynamique quantique" du CNRS.

Pour tout renseignement complémentaire, veuillez contacter les organisateurs, Hakim Boumaza, Mathieu Lewin ou Stéphane Nonnenmacher.

Prochain séminaire le lundi 17 juin 2019 en salle 314 (3e étage)
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 11h15 - 12h15 Takuya Watanabe (Ritsumeikan)
Widths of resonances above an energy-level crossing


We study the existence and location of the resonances of a 2x2 semiclassical system of coupled Schrödinger operators, in the case where the two electronic levels cross at some point, and one of them is bonding, while the other one is anti-bonding. Considering energy levels just above that of the crossing, we find the asymptotics of both the real parts and the imaginary parts of the resonances close to such energies. In this talk, we would like give the result above and compare it with our previous works where we considered energy levels around that of the crossing.
This talk is based on joint works with S. Fujiié (Ritsumeikan) and A. Martinez (Bologna).

14h - 15h Mona Ben Said (Paris-Nord)
Compactness of the resolvent for Kramers-Fokker-Planck operators

This talk is devoted to the study of some spectral properties and compactness criteria for the resolvent of Kramers-Fokker-Planck operators, which will be denoted by KV . I will speak in particular about the results obtained from a joint work with Francis Nier and Joe Viola on the case of a polynomial potential V of degree less than 3. Then based on this work, I will present my recent results which concerns compactness criteria for the resolvent of the operator
KV with more general potentials.
 15h15 - 16h15 Stephan De Bièvre (Lille)
Measuring the Non-Classicality of the Quantum States of a Bosonic Field with Ordering Sensitivity

In quantum optics, a classical state of the quantized electromagnetic field is a mixture of coherent states. When a state is not classical, it is of importance to establish how strongly nonclassical it is. We will present a recently introduced distance-based measure for the nonclassicality of the states of such fields, and show its advantages over existing such measures.
We define for that purpose the operator ordering sensitivity of the state which evaluates the sensitivity to operator ordering of the Renyi entropy of its quasi-probabilities and which measures the oscillations in its Wigner function. Through a sharp control on the operator ordering sensitivity of classical states we obtain a precise geometric image of their location in the density matrix space allowing us to introduce the aforementioned measure of nonclassicality. Its
properties will be illustrated with a variety of examples.
Joint work with D.Horoshko, G.Patera and M.Kolobov

Prochaines dates prévues:

October 2019:

Informations pratiques: Plan d'accès à l'IHP.

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Dernière mise à jour: 29 mai 2019
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