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Updated: Jul 13, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Order-chaos transition in correlation diagrams and quantization of period orbits
F J Arranz1, J Montes1,2, F Borondo2
1Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, 28040 Madrid, Spain.
Abstract:
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)0031-900710.1103/PhysRevLett.80.944] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing the Planck constant, we induced a transition from order to chaos, in which scarred wave functions 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 straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.
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