Calculation of Highly Excited Degenerate Eigenstates of a Chaotic System in Energy Windows - Revuelta, F.; Vergini, E.; Benito, R. M.; Borondo, F. (Discontinuity, Nonlinearity, and Complexity, 2026)
In this work, we calculate degenerate eigenstates of a coupled quartic oscillator with a high degree of chaoticity in a narrow energy window. For this purpose, we extend the range of applicability of the scar functions defined by us in F. Revuelta et al., Phys. Rev. E 102, 042210 (2020) to this more complicated case. Our method allows the reconstruction of individual eigenstates in terms of the shortest unstable periodic orbits of the system. As in the case of nondegenerate states, the basis size is of the same order of the number of computed eigenfunctions and depends on the ratio between the Heisenberg and the Ehrenfest times.