Quantum Chaos Control by Complex Trajectories

TL;DR

This paper introduces a novel approach to analyze and control quantum chaos by extending classical mechanics into the complex domain, enabling the use of classical chaos methods for quantum systems.

Contribution

It develops a complex mechanics framework to model quantum motions and applies sliding-mode control to suppress chaos in a quantum harmonic oscillator.

Findings

Chaotic quantum motions can be stabilized into periodic motions.

Chaos synchronization is achievable despite initial condition variations.

Signatures of chaos validate the control process.

Abstract

In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect Newton's world to the quantum world by the complex mechanics so that quantum chaos can be analyzed and controlled by the complex-extended Newtonian mechanics. Through the bridge of complex mechanics, in this article, we model quantum motions for 2D charged anisotropic harmonic oscillator by complex-valued dynamic equations, based on which quantum chaos can be analyzed by using well-known methods used in classical chaos. With the established quantum dynamic model, we then apply the sliding-mode control method to control the chaotic quantum behavior of the considered quantum system. The simulation results show that chaotic motions can be changed into periodic motions by the proposed chaos control and meanwhile, chaos synchronization can be achieved in the presence of variations of initial conditions. Several signatures of chaos are introduced here to justify the chaos of the periodicity process under the sliding-mode control law.