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We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory. By introducing a fractal approach to describe the chaotic dynamical behavior of the ionization, we identify the fractal self-similarity structure of the escape time versus the distribution of the initial launch angles of electrons, and find that the self-similarity region shifts toward larger initial launch angles with a decrease in the scaled energy. We connect the fractal structure of the escape time plot to the escape dynamics of ionized electrons. Of particular note is that the fractal dimensions are sensitively controlled by the scaled energy and magnetic field, and exhibit excellent agreement with the chaotic extent of the ionization systems for both helium and hydrogen Rydberg atoms. It is shown that, besides the electric and magnetic fields, core scattering is a primary factor in the fractal dynamics.

In this paper, we theoretically study the ballistic transport through a weakly open circular mesostructure within the framework of pseudopath semiclassical approximation. By defining the interference factor and comparing it numerically with the transmission amplitude, we demonstrate that the fluctuations in transmission amplitude are mainly due to the interference effects between different classical trajectories. In addition, we calculate the Fano factor versus cutoff length of classical trajectories in the energy domain to illustrate that the fluctuations in transmission amplitude mainly arise from the contribution of short-length classical trajectories. We further show that the transmission length power spectra not only associate with a lot of classical trajectories but with a series of nonclassical trajectories due to the diffraction scattering effects. Moreover, we show that the classical trajectories distributed in the mode–mode coupling function give the largest contribution to the corresponding transmission amplitude. We hope that our results and analysis can be used to reveal new effects of mesoscopic systems and to provide theoretical basis for the design of mesoscopic devices.

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