A periodic orbit basis for the Quantum Baker Map

TL;DR

This paper introduces a basis constructed from quantum states related to classical periodic orbits of the Quantum Baker Map, simplifying eigenstate descriptions and improving with short-time propagation along manifolds.

Contribution

It presents a novel basis based on classical periodic orbits for the quantum Baker Map, enhancing eigenstate analysis and connecting classical and quantum dynamics.

Findings

Basis simplifies eigenstate descriptions

Inclusion of short-time propagation improves basis quality

Participation ratio quantifies basis effectiveness

Abstract

A set of quantum states, dynamically related to the classical periodic orbits of a chaotic map, is used as a basis in which the description of the eigenstates of its quantum version is greatly simplified. This set can be improved with the inclusion of short time propagation along the stable and unstable manifolds of the periodic orbits resulting in a construction similar to the scar functions of Vergini (Jour. Phys. A \textbf{33}, (2000) 4709). The average participation ratio is used to quantify the quality of the basis.