Chaotic photon spheres in non-Euclidean billiard

With the advancement in understanding of the physics inside chaotic systems, chaos has been harnessed from a nuisance to a beneficial factor in optical devices. Light–matter interaction in chaotic systems has been utilised for improving broadband energy harvesting and momentum transformations, achieving light localization beyond diffraction limit and even stabilizing the dynamics of high power laser. While extensive study about wave chaos has been made in deformed microcavities, investigation of how chaos dynamics evolves in curved space manifold remains elusive. Here, we study the non-Euclidean billiard of a torus-like manifold, which is a closed 2D cavity system with effective periodic boundaries. The ray chaotic behaviours on the deformed toroidal surface are explored using the geodesic equation. By tuning the deformation parameter of the torus, we observe the transition of the billiard from the ordered phase state to mixed phase states and then complete ray chaos. The photon sphere of the torus is identified as the transition position from ordered states to chaotic states. Compared with other chaotic behaviours resulted from the random scattering inside deformed cavities, we demonstrate chaotic dynamics purely on a curved surface, which may shed light on the better understanding of chaos in optics.

Regularities in the spectrum of chaotic p-modes in rapidly rotating stars

Context. Interpreting the oscillations of massive and intermediate mass stars remains a challenging task. In fast rotators, the oscillation spectrum of p-modes is a superposition of sub-spectra which corresponds to different types of modes, among which island modes and chaotic modes are expected to be the most visible. This paper is focused on chaotic modes, which have not been thoroughly studied before. Aims. We study the properties of high frequency chaotic p-modes in a polytropic model. Unexpected peaks appear in the frequency autocorrelations of the spectra. Our goal is to find a physical interpretation for these peaks and also to provide an overview of the mode properties. Methods. We used the 2D oscillation code “TOP” to produce the modes and acoustic ray simulations to explore the wave properties in the asymptotic regime. Using the tools developed in the field of quantum chaos (or wave chaos), we derived an expression for the frequency autocorrelation involving the travel time of acoustic rays. Results. Chaotic mode spectra were previously thought to be irregular, that is, described only through their statistical properties. Our analysis shows the existence, in chaotic mode spectra, of a pseudo large separation. This means that chaotic modes are organized in series, such that the modes in each series follow a nearly regular frequency spacing. The pseudo large separation of chaotic modes is very close to the large separation of island modes. Its value is related to the sound speed averaged over the meridional plane of the star. In addition to the pseudo large separation, other correlations appear in the numerically calculated spectra. We explain their origin by the trapping of acoustic rays near the stable islands.