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# Quantum and Classical Dynamics Seminars

Seminar organized by the two teams of the group **Classical and Quantum Dynamical Systems**.

**Person in charge:** ** Yavar KIAN **

**Dedicated Day:** Wednesday, 14:00

**Place: ** CPT, Amphitheater on the 5th floor

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## Next Quantum and Classical Dynamics Seminars

### Wednesday 23 January

14h00 – 15h00, CPT, Amphi 5

### Spectral theory and limiting amplitude principle for Maxwell’s equations at the interface of a metamaterial

#### Maxence Cassier (Institut Fresnel, Université d'Aix-Marseille)

In this talk, we are interested in a transmission problem between a dielectric and a metamaterial. The question we consider is the following: does the limiting amplitude principle hold in such a medium? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. An answer is proposed here in the case of a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill respectively complementary half-spaces. In this context, we reformulate the time-dependent Maxwell’s equations as a conservative Schr¨odinger equation and perform its complete spectral analysis. This permits a quasi-explicit representation of the solution via the ”generalized diagonalization” of the associated unbounded self-adjoint operator. As an application of this study, we show finally that the limiting amplitude principle holds except for a particular fequency characterized by a ratio of permittivities and permeabilities equal to −1 across the interface. This frequency is a resonance of the system and the response to this excitation blows up linearly in time. This is a common work with Christophe Hazard (Poems team) and Patrick Joly (Poems team).