Inverse problem of analog gravity systems II: Rotation and energy-dependent boundary conditions

TL;DR

This paper develops a parameter-free inverse method using WKB analysis to relate transmission spectra with effective potentials in rotating analog gravity systems, aiding experimental exploration of boundary conditions.

Contribution

It extends previous results to include rotation and energy-dependent boundary conditions, providing a new approach to reconstruct effective potentials from spectral data.

Findings

Method accurately reconstructs effective potentials with similar spectral features.

Applicable to rotating vortex systems modeling astrophysical objects.

Highlights potential for experimental studies of boundary conditions in analog gravity.

Abstract

In this work, we study the inverse problem of analog gravity systems which admit rotation and energy-dependent boundary conditions. By extending two recent results, we provide a recipe that allows one to relate resonant transmission spectra with effective potentials and even reconstruct the boundary condition at the core. Our methodology is based on the WKB method and the identification of universal features in the transmission. One of the main advantages of this method is that it is parameter-free, and relies only on general properties of the underlying potential, instead of specific models. While the reconstruction of underlying potentials is generally not uniquely possible, the inverse method provides effective potentials with similar spectral properties to the original one. To demonstrate the accuracy and scope of our method, we apply it to a rotating imperfect draining vortex, which has been proposed as an analog system to astrophysical extreme compact objects. We conclude that the capability to explore energy-dependent boundary conditions could be of interest for experimental studies of such systems.