Quantum-Chaotic Evolution Reproduced from Effective Integrable Trajectories

TL;DR

This paper demonstrates that effective integrable trajectories can accurately reproduce quantum chaotic evolution, offering improved semiclassical approximations even in predominantly chaotic systems.

Contribution

The authors construct integrable approximants for chaotic systems and show they outperform traditional chaotic trajectory-based methods in semiclassical quantum evolution.

Findings

Integrable approximants reproduce quantum oscillations effectively.

Semiclassical approximations based on integrable trajectories outperform chaotic ones.

Effective integrable trajectories remain valid even in broad chaotic regions.

Abstract

Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum systems using semiclassical approximations based alternatively on the chaotic and on the integrable trajectories. It is found that the latter reproduce the quantum oscillations and provide superior approximations even when the initial coherent state is placed in a broad chaotic region. Time regimes are then accessed in which the propagation based on the system's exact chaotic trajectories breaks down.