Chaotic dynamics of the hydrogen atom in a space-dependent electric field

We study the chaotic dynamics of the hydrogen atom in a space-dependent gradient electric field. We use the Poincaré surface of section (PSS) and the Lyapunov exponents to characterize chaotic dynamics. The dynamical character of this system is studied and the regular-chaos transition is found when the system passes from the non-integrable case to the integrable one. It is found that for a given gradient electric field, this system has a critical scaled energy ${\epsilon }_s.$ When the scaled energy $\epsilon ⩽{\epsilon }_s,$ the structure of the whole phase space is nearly regular. However, as the scaled energy $\epsilon >{\epsilon }_s,$ chaotic structures appear in the PSS. As the scaled energy is very large, the whole PSS is chaotic. The chaotic property of this system is further verified by the positive value of the maximum Lyapunov exponent. In addition, we show that with increasing electric field gradient the dynamics of this system becomes increasingly chaotic. Our work provides an example to study the chaotic dynamics of the hydrogen atom by using the space-dependent electric field. We hope that our results can guide the future experimental researches about the dynamical property of the atoms or molecules in the non-uniform external fields. (paper)