# gst: chaotic billiards inside mixed curvatures

<< The boundary of a billiard system dictates its dynamics, which can be integrable, mixed, or fully chaotic. >>️

This AA study << introduces two such billiards: a bean-shaped billiard and a peanut-shaped billiard, the latter being a variant of Cassini ovals. Unlike traditional chaotic billiards, these systems incorporate both focusing and defocusing regions along their boundaries, with no neutral segments. >>

AA << examine both classical and quantum dynamics of these billiards and observe a strong alignment between the two perspectives. For classical analysis, the billiard flow diagram and billiard map reveal sensitivity to initial conditions, a hallmark of classical chaos. In the quantum domain, (AA) use nearest-neighbour spacing distribution and spectral complexity as statistical measures to characterise chaotic behaviour. >>

<< Both classical and quantum mechanical analysis are in firm agreement with each other. One of the most striking quantum phenomena (They) observe is the eigenfunction scarring (both scars and super-scars). Scarring phenomena serve as a rich visual manifestation of quantum and classical correspondence, and highlight quantum suppression chaos at a local level. >>

Pranaya Pratik Das, Tanmayee Patra, Biplab Ganguli. Manifestations of chaos in billiards: the role of mixed curvature. arXiv: 2501.08839v1 [nlin.CD]. Jan 15, 2025.

https://arxiv.org/abs/2501.08839

Also: billiard, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, chaos