Collective oscillations in classical nonlinear response of a chaotic system

TL;DR

This paper analyzes how classical nonlinear responses behave in strongly chaotic systems, revealing exponential decay and collective resonances, with analytical calculations illustrating these phenomena and their relevance to spectroscopy.

Contribution

It provides the first analytical calculation of linear and second-order responses in a chaotic system, linking response features to collective resonances beyond classical trajectories.

Findings

Nonlinear response vanishes at large times in chaotic systems

Response exhibits collective resonances not tied to periodic trajectories

Analytical results applicable to spectroscopic data interpretation

Abstract

We consider classical response in a strongly chaotic (mixing) system. As opposed to the case of stable dynamics, the nonlinear classical response in a chaotic system vanishes at large times. The physical behavior of the nonlinear response is attributed to the exponential time dependence of the stability matrix. The response also reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We calculate analytically linear and second-order response in a simple chaotic system and argue on the relevance of the model for interpretation of spectroscopic data.