The transition to chaos of coupled oscillators: An operator fidelity susceptibility study

TL;DR

This study investigates how operator fidelity susceptibility can detect the transition from regular to chaotic behavior in coupled oscillators, providing a numerical method to identify chaos in quantum systems.

Contribution

The paper introduces a numerical analysis of operator fidelity susceptibility to identify chaos in a coupled oscillator model, linking theoretical measures to observable transitions.

Findings

OFS detects the transition between regular and chaotic regimes.

A local minimum in OFS terms marks the limit of perturbation theory applicability.

The model relates to hydrogen atom behavior in magnetic fields.

Abstract

The operator fidelity is a measure of the information-theoretic distinguishability between perturbed and unperturbed evolutions. The response of this measure to the perturbation may be formulated in terms of the operator fidelity susceptibility (OFS), a quantity which has been used to investigate the parameter spaces of quantum systems in order to discriminate their regular and chaotic regimes. In this work we numerically study the OFS for a pair of non-linearly coupled two-dimensional harmonic oscillators, a model which is equivalent to that of a hydrogen atom in a uniform external magnetic field. We show how the two terms of the OFS, being linked to the main properties that differentiate regular from chaotic behavior, allow for the detection of this model's transition between the two regimes. In addition, we find that the parameter interval where perturbation theory applies is delimited from above by a local minimum of one of the analyzed terms.