Generalising hyperboloidal methods for non-relativistic systems

Abstract

The compactified hyperboloidal method is a powerful tool for calculating quasinormal mode (QNM) spectra in relativistic settings. However, there has been increasing interest in the QNMs of non-relativistic systems, motivated in part by the ongoing development of table-top analogue gravity experiments featuring weak dispersion. I will begin by generalising the QNM eigenvalue problem for non-relativistic systems, and I will demonstrate how the hyperboloidal method is extended to enable direct computation of QNM spectra in systems obeying a Schrödinger equation. Finally, I will discuss progress on further extending the method to generalised wave equations, with comments on potential applications.