# Periodic Orbit Scar in Propagation of Wavepacket

## TL;DR

This paper investigates how wavepackets in a stadium billiard localize along unstable periodic orbits, revealing a scar phenomenon explained by semiclassical approximation and classical action contributions.

## Contribution

It demonstrates the emergence of wavepacket scars along classical unstable periodic orbits and clarifies their semiclassical origin, extending understanding of quantum-classical correspondence.

## Key findings

- Wavepackets launched along orbits form scars on unstable periodic orbits.
- Localization is explained via semiclassical approximation and classical action piling.
- Multiple energy states contribute to the scar enhancement.

## Abstract

This study analyzed the scar-like localization in the time-average of a timeevolving wavepacket on the desymmetrized stadium billiard. When a wavepacket is launched along the orbits, it emerges on classical unstable periodic orbits as a scar in the stationary states. This localization along the periodic orbit is clarified through the semiclassical approximation. It essentially originates from the same mechanism of a scar in stationary states: the piling up of the contribution from the classical actions of multiply repeated passes on a primitive periodic orbit. To create this enhancement, several states are required in the energy range, which is determined by the initial wavepacket.