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Lundi 3 Juillet
| Heure: |
14:00 - 15:00 |
| Lieu: |
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
EDP & Physique mathématique - Spectral gap for harmonic and weakly anharmonic chain of oscillators - |
| Description: |
Angeliki Menegaki We
consider one-dimensional chains and multi-dimensional networks of
harmonic oscillators coupled to two Langevin heat reservoirs at
different temperatures. Each particle interacts with its nearest
neighbours by harmonic potentials and all individual particles are
confined by harmonic potentials, too. In previous works we investigated
the sharp N-particle dependence of the spectral gap of the associated
generator in different physical scenarios and for different spatial
dimensions. We also obtained estimates on the gap after perturbing
weakly the quadratic potentials, through a  Log-Sobolev
Inequality. In this talk I will present new results on the behaviour of
the spectral gap when considering longer-range interactions in the
purely harmonic chain. In particular, depending on the strength of the
longer-range interaction, there are different regimes appearing where
the gap drastically changes behaviour but even the hypoellipticity of
the operator breaks down. |
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