Superscar states in rational polygon billiards - a reality or an illusion?

TL;DR

This paper investigates the superscar phenomena in rational polygon billiards using semiclassical wave functions, concluding that superscars are natural features of classical trajectories and do not require the superscar state hypothesis.

Contribution

The study demonstrates that superscars in rational polygon billiards arise from classical skeletons and do not violate quantum principles, challenging prior interpretations.

Findings

Superscars are natural properties of semiclassical wave functions built on classical skeletons.

Superscar effects are present in various rational polygon billiards, including integrable and pseudointegrable cases.

Superscars do not violate quantum mechanics principles, contrary to previous claims.

Abstract

The superscars phenomena (Heller, E.J., Phys. Rev. Lett. 53, (1984) 1515) in the rational polygon billiards (RPB) are analysed using the high energy semiclassical wave functions (SWF) built on classical trajectories forming skeletons. Considering examples of the pseudointegrable billiards such as the Bogomolny-Schmit triangle, the parallelogram and the L-shape billiards as well as the integrable rectangular one the constructed SWFs allow us to verify the idea of Bogomolny and Schmit (Phys. Rev. Lett. 92 (2004) 244102) of SWFs (superscars) propagating along periodic orbit channels (POC) and vanishing outside of them. It is shown that the superscars effects in RPB appear as natural properties of SWFs built on the periodic skeletons. The latter skeletons are commonly present in RPB and are always composed of POCs. The SWFs built on the periodic skeletons satisfy all the basic principles of the quantum mechanics contrary to the superscar states of Bogomolny and Schmit which break them. Therefore the superscars effects need not to invoke the idea of the superscar states of Bogomolny and Schmit at least in the cases considered in our paper.