Hidden timescale in the response of harmonically driven chaotic systems

TL;DR

This paper investigates the non-linear spectral broadening in driven chaotic systems, revealing a hidden timescale linked to classical phase-space dynamics that challenges traditional Fermi-golden-rule predictions.

Contribution

It identifies a previously unrecognized timescale governing spectral smearing in driven chaotic systems, emphasizing the role of classical dynamics over quantum perturbation theory.

Findings

Fermi-golden-rule fails to predict non-linear transition widths

Classical phase-space dynamics determine the hidden timescale

Spectral line-shape broadening is governed by classical effects

Abstract

Linear response theory relates the response of a system to the power-spectrum of its fluctuations. However, the response to external driving in realistic models exhibits a pronounced non-linear blurring of the spectral line-shape. Considering a driven Bose-Hubbard trimer model we figure out what is the hidden time scale that controls this smearing effect. Contrary to conventional wisdom, the Fermi-golden-rule picture fails miserably in predicting the non-linear width of the transitions. Instead, if the system has a classical limit, the determination of the hidden time scale requires taking into account the underlying classical phase-space dynamics.