The Edge of Quantum Chaos

TL;DR

This paper explores the boundary between regular and chaotic quantum dynamics, identifying a power law decay in state overlap that marks the edge of quantum chaos, with implications for understanding quantum-classical correspondence.

Contribution

It introduces a quantitative characterization of the quantum chaos border using nonextensive entropy and overlap decay analysis, linking quantum and classical chaos.

Findings

Overlap decay follows a power law near the chaos border.

The decay fits a nonextensive entropy model with parameter q.

The quantum chaos border correlates with classical chaos onset.

Abstract

We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with $[1+(q-1) (t/\tau)^2]^{1/(1-q)}$ (with the nonextensive entropic index $q$ and $\tau$ depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.