Spectral analysis of the spin-boson Hamiltonian with two photons for arbitrary coupling

We study the spectrum of the spin-boson model with two photons in $\mathbb{R}^d$ for arbitrary coupling $\alpha>0$. It is shown that the discrete spectrum is finite and the essential spectrum consists of a half-line the bottom of which is a unique zero of a simple Nevanlinna function. Besides the simplicity and more abstract nature of our approach, the main novelty is the achievement of these results under "minimal" regularity conditions on the photon dispersion and the coupling function.Comment: 16 page

Sharp spectral bounds for complex perturbations of the indefinite Laplacian

We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real-valued potentials. For $L^1$-potentials, we obtain optimal spectral enclosures which accommodate also embedded eigenvalues, while our result for $L^p$-potentials yield sharp spectral bounds on the imaginary parts of eigenvalues of the perturbed operator for all $p\in[1,\infty)$. The sharpness of the results are demonstrated by means of explicit examples.Comment: References added before Theorem 2 and