Resonances as viscosity limits for black box perturbations

TL;DR

This paper demonstrates that the complex absorbing potential method effectively computes scattering resonances for a broad class of black box perturbations of the Laplacian, unifying various scattering problems.

Contribution

It extends the applicability of the CAP method to abstract black box perturbations that can be analytically continued, covering diverse scattering scenarios.

Findings

CAP method applies to a wide class of black box perturbations

Unifies treatment of obstacle and surface scattering problems

Provides a framework for analyzing resonances in complex geometries

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.