The short periodic orbit method for excited chaotic eigenfunctions

TL;DR

This paper introduces a novel method utilizing wavefunctions localized on unstable periodic orbits to efficiently compute excited chaotic eigenfunctions across energy ranges, demonstrated on a chaotic oscillator.

Contribution

It presents a new approach using localized wavefunctions on unstable periodic orbits for calculating excited eigenfunctions in chaotic systems.

Findings

Efficient basis set reduces computational complexity.

Method applicable to arbitrary energy windows.

Successful demonstration on a chaotic oscillator.

Abstract

In this paper [published in Phys. Rev. E 102, 042210 (2020)], a new method for the calculation of excited chaotic eigenfunctions in arbitrary energy windows is presented. We demonstrate the feasibility of using wavefunctions localized on unstable periodic orbits as efficient basis sets for this task in classically chaotic systems. The number of required localized wavefunctions is only of the order of the ratio t H /t E , with t H the Heisenberg time and t E the Ehrenfest time. As an illustration, we present convincing results for a coupled two-dimensional quartic oscillator with chaotic dynamics.