Coulomb-interaction-induced quantum irregularity in two electrons within a hard-walled circular billiard

We investigate quantum mechanics of Coulomb-interacting two electrons within a hard-walled circular billiard. Despite the integrability of a system of non-interacting electrons confined within the highly symmetric billiard, the Coulomb interaction can make the system non-integrable and chaotic.The energy spectra show the interaction-induced level statistics which is in an overall agreement with the Wigner (GOE) level spacing distribution and spectral rigidity. The Brody parameter as a function of the effective Coulomb interaction is evaluated, which quantifies a continuous transition from the Poisson to Wigner level spacing distributions. The case of the zero total angular momentum needs an extra classification of eigenfunctions to remove the degeneracy, which is required by the time-reversal symmetry of the system. The interaction-induced breaking of the spatial symmetry which leads to quantum irregularity can be visualized by using the two-particle correlation function and the single-particle density for eigenstates.