Mathematical Physics and Harmonic Analysis Seminar

Date: March 21, 2025

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Danko Moisés Aldunate Bascuñán

Title: Nonlinear Dirac equation: characterization of a gap property for the linearized 1D Soler model

Abstract: We establish for the 1D Soler model with power nonlinearities $f(s)=s|s|^{p-1}$, $p>0$, that the upper-right block operator~$L_0$ of the linearized operator satisfies: its ground states $-2\omega$ and $0$ are its only two eigenvalues in the gap of its essential spectrum if only if $p\geq1$. Our second main result is the simplicity of generalized eigenfunction at the threshold of the essential spectrum for Dirac operators with potential. These results apply in particular to lower-left block operator~$L_\mu$.