Order-chaos transition in correlation diagrams and quantization of period orbits

• Published in: arXiv.org
• Main Authors: Arranz, F J, Montes, J, Borondo, F
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 25.01.2024
• Subjects: Chaos theory; Correlation; Eigenvectors; Orbits; Physics - Chaotic Dynamics; Physics - Chemical Physics; Physics - Quantum Physics; Plancks constant; Wave functions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2401.14465

Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing Planck constant, we induced a transition from order to chaos, in which scarred wavefunctions appeared as the interaction of pairs of eigenstates in broad avoided crossings, forming a well defined frontier in the correlation diagram. In this paper, we demonstrate that this frontier can be obtained by means of the semiclassical quantization of the involved scarring periodic orbits. Additionally, in order to calculate the Maslov index of each scarring periodic orbit, which is necessary for the semiclassical quantization procedure, we introduce a novel straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.