Fractals and Scars on a Compact Octagon

TL;DR

This paper explores how fractals and quantum scars emerge from chaotic dynamics in a finite 2D octagon universe, highlighting their persistence and subtle implications in quantum behavior.

Contribution

It provides a detailed characterization of fractals and scars in a compact octagon, linking classical chaos to quantum wave function features.

Findings

Fractals form from chaotic classical motion in the octagon.

Quantum scars are present but weak in this system.

Fractals and scars may have subtle implications in finite universes.

Abstract

A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact 2-dimensional octagon. In the classical to quantum transition, the underlying fractal can persist in the form of scars, ridges of enhanced amplitude in the semiclassical wave function. Although the scarring is weak on the octagon, we suggest possible subtle implications of fractals and scars in a finite universe.