SIPo: Spectral Stability in the one-dimensional nonlinear Dirac equation with Soler-type nonlinearity

Abstract:

We study the spectral properties of the Dirac operator L_0 obtained by linearizing the one-dimensional Soler model around standing waves with power nonlinearity f(s) = s|s|^{p-1}, p > 0. We give a sharp characterization of the spectral gap. If p ≥ 1, the gap contains no eigenvalues other than the symmetry-induced energies -2ω and 0. If 0 < p < 1, additional eigenvalues bifurcate from the thresholds of the essential spectrum and enter the gap. We further prove that the thresholds are never eigenvalues for any p > 0 and that there are no resonances for p > 1.

Speaker: Danko Aldunate (CMM, U. de Chile)