Spectrum of the Dirac operator in thin domains: waveguides and planar domains defined by the graph of a function

par Thomas Ourmières-Bonafos (Marseille)

lundi 11 mai 2026, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

In this talk, we study the spectrum of the Dirac operator in planar domains equipped with infinite mass boundary conditions. We consider two settings: waveguides and domains defined as planar regions lying below the graph of a function. Our goal is to derive asymptotic expansions of the eigenvalues in regimes where these domains become thin.

 

We will show how tools from semiclassical analysis and pseudodifferential calculus provide a powerful framework for addressing such problems. In particular, we employ a dimension reduction technique, known as the Grushin method, which yields an effective operator in both settings. The originality of this approach lies in the fact that the symbols of the operators under consideration are operator-valued, acting on functions of a single variable. Using this method, we also obtain refined information on the associated eigenmodes, including elliptic estimates and microlocalization results.

 

This are joint works with  L. Le Treust, L. Mazzouza, F. Monteghetti et N. Raymond.