Computing Quantum Mean Values in the Deep Chaotic Regime

TL;DR

This paper introduces a novel approach for computing quantum mean values in strongly chaotic regimes, overcoming limitations of traditional semiclassical methods and achieving unprecedented accuracy in complex quantum systems.

Contribution

The authors develop a new method that addresses conceptual issues in semiclassical approximations, enabling precise quantum calculations in deep chaotic regimes.

Findings

The new approach achieves unprecedented accuracy in deep chaotic regimes.

Standard semiclassical methods like Herman-Kluk produce numerical noise in this regime.

The method enhances understanding of interference contributions in quantum chaos.

Abstract

We study the time evolution of mean values of quantum operators in a regime plagued by two difficulties: The smallness of $\hbar$ and the presence of strong and ubiquitous classical chaos. While numerics become too computationally expensive for purely quantum calculations as $\hbar \to 0$, methods that take advantage of the smallness of $\hbar$ -- that is, semiclassical methods -- suffer from both conceptual and practical difficulties in the deep chaotic regime. We implement an approach which addresses these conceptual problems, leading to a deeper understanding of the origin of the interference contributions to the operator's mean value. We show that in the deep chaotic regime our approach is capable of unprecedented accuracy, while a standard semiclassical method (the Herman-Kluk propagator) produces only numerical noise. Our work paves the way to the development and employment of more efficient and accurate methods for quantum simulations of systems with strongly chaotic classical limits.