Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincaré surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy \varepsilon _\rm c , for \varepsilon < \varepsilon _\rm c , the system is near-integrable, and as the decrease of \varepsilon the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if \varepsilon>\varepsilon_\rm c, with the increase of \varepsilon, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.