Resonances as viscosity limits for black box perturbations

Abstract

We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to an abstractly defined class of black box perturbations of the Laplacian in $\mathbb{R}^n$ which can be analytically extended from $\mathbb{R}^n$ to a conic neighborhood in $\mathbb{C}^n$ near infinity. The black box setting allows a unifying treatment of diverse problems ranging from obstacle scattering to scattering on finite volume surfaces.