2025/10/10 by Quiroz-Juarez, Mario A., Zurita, Marco A., Olivares-Pilon, Horacio +1
#Chaotic Dynamics (nlin.CD) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2510.09910
We analyze how quantum mechanics reinstates confinement in Hamiltonian systems that are classically unstable and exhibit chaotic dynamics. Specifically, we consider two paradigmatic models: the Contopoulos Hamiltonian, an isotropic oscillator perturbed by the quartic coupling α x2y2, and the purely quartic Yang--Mills Hamiltonian H=\tfrac12(px2+py2)+α x2y2. Classical dynamics, characterized through Poincaré sections, Lyapunov exponents, and periodic orbits, reveals distinct escape mechanisms: in the Contopoulos system, trajectories destabilize along the diagonal valleys x=± y for α<0, whereas in the Yang--Mills case with α>0, escape occurs along the coordinate axes x=0 or y=0. In sharp contrast, the quantum Yang--Mills Hamiltonian with α>0 admits only discrete, normalizable eigenstates. Semiclassical WKB and full two--dimensional analyses further show that these quantum states are localized along the classical escape channels, illustrating how transverse zero--point motion generates an effective confining barrier. Our study combines global Lyapunov--exponent heat maps with high--precision quantum spectra obtained via variational and Lagrange--mesh methods, providing quantitatively controlled results across regimes. In addition, we corroborate the classical predictions through analog electronic simulations based on operational--amplifier circuit models, offering an experimentally inspired validation of the theoretical framework.