Effects of angular momentum on eigenvalue statistics in a two-dimensional quantum system with rotational symmetry.

Abstract

We study the influence of angular momentum on the eigenvalue statistics of a two-dimensional quantum system with rotational symmetry composed of concentric Dirac-δ barriers inside an infinite circular well. Using the transfer-matrix method, we computed extensive ensembles of eigenvalues for different transmission probabilities, numbers of barriers, and angular quantum numbers m. The unfolded spectra were analyzed by level-spacing distributions, number variance, and eigenstate participation. As the transmission increases, the system undergoes a transition from Poisson to Gaussian-orthogonal-ensemble statistics, whereas the angular momentum modifies the fine structure of spectral correlations and eigenfunction delocalization. In particular, high m values enhance the number variance and modulate level repulsion at low transmission. These findings show that even in rotationally symmetric systems, angular momentum acts as an internal parameter that subtly reshapes the signatures of quantum chaos in singular potentials.