Szegö-type inequality for the 2-D Dirac operator with infinite mass boundary conditions

Abstract: In this talk, we will discuss spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we derive a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\H{o} type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. We will also present strong numerical evidence supporting the validity of a Faber-Krahn type inequality.

This talk is based on a joint work with Pedro Antunes, Rafael Benguria, and Thomas Ourmi\`{e}res-Bonafos.

mathematical physicsanalysis of PDEsspectral theory

Audience: researchers in the topic

Quantum Circle