Chaotic dynamics and the recurrence spectra of the Rydberg hydrogen atom near a dielectric surface

The classical electronic motion of the Rydberg hydrogen atom near a dielectric surface has been studied by using the Poincaré surfaces of section method and the closed orbit theory. The structure and evolution of the phase space as a function of the scaled energy is explored extensively by means of the Poincaré surfaces of section. The results suggest that when the scaled energy is less than the critical energy epsilon(s), the whole phase space structure is regular. However, when the energy is larger than epsilon(s), chaotic motions appear. The recurrence spectra of this system have also been calculated. The results show that, for a given scaled energy larger than the critical energy epsilon(s), when the dielectric constant alpha is small, the influence of the dielectric surface can be neglected and the number of closed orbits is very small. With the increase of the dielectric constant alpha, the effect of the dielectric surface becomes significant, the number of closed orbits increases, and there are more peaks in the recurrence spectra. When alpha = 1.0, the recurrence spectra approach the case of the Rydberg hydrogen atom near a metallic surface. This study provides a new method to explore the dynamic behavior of the Rydberg atom interacting with a dielectric surface.