Wave function statistics for ballistic quantum transport through chaotic open billiards: Statistical crossover and coexistence of regular and chaotic waves

For ballistic transport through chaotic open billiards, we implement accurate fully quantal calculations of the probability distributions and spatial correlations of the local densities of single-electron wave functions within the cavity. We find wave-statistical behaviors intrinsically different from those in their closed counterparts. Chaotic-scattering wave functions in open systems can be quantitatively interpreted in terms of statistically independent real and imaginary random fields in the same way as for wave-function statistics of closed systems in the time-reversal symmetry-breaking crossover regime. We also discuss perceived statistical deviations, which are attributed to the coexistence of regular and chaotic waves and given analytical explanations.