Description of quantum chaotic systems by coherent states

Jiangbin Gong, Gong-ou Xu, Rui-hua Xie

We give here a physical picture that exponential instability can occur with the coherence of states preserved in a mixed quantum classical description. Taking advantage of the concept of the geometrical structure of a quantum system, we are able to illustrate our ideas with some examples in a simple manner. This kind of chaos may be important for further investigations of chaotic behaviors in systems with both quantum and classical degrees of freedom.

K. N. Alekseev, G. P. Berman

M. S. Santhanam

P. Lebœuf, André Voros

The quantisation of the two-dimensional toric and spherical phase spaces is considered in analytic coherent state representations. Every pure quantum state admits therein a finite multiplicative parametrisation by the zeros of its Husimi function. For eigenstates of quantised systems, this description explicitly reflects the nature of the underlying classical dynamics: in the semiclassical regime, the distribution of the zeros in the phase space becomes one-dimensional for integrable systems, and highly spread out (conceivably uniform) for chaotic systems. This multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems.

Ronald F. Fox

Jincheng Zhang

This paper investigates the application of quantum coherence to the analysis of chaotic systems. The core claim is that leveraging the inherent properties of quantum coherence can reveal hidden patterns within chaotic systems. This work models chaotic systems as quantum systems and utilizes quantum coherence to identify critical parameters and potential control methods. The novelty lies in exploring the intersection of quantum mechanics and chaos theory, presenting a new approach to analyzing complex, nonlinear dynamics. We present a theoretical framework, focusing on the impact of quantum coherence on the behavior of specific chaotic systems, without experimental validation. The analysis provides insights into the potential for quantum-inspired control strategies and a deeper understanding of the underlying mechanisms driving chaotic dynamics. The central mathematical framework involves Hamiltonian operators, wave functions, and coherence measures, emphasizing the shift from classical deterministic descriptions to a quantum probabilistic one.