Perspectives on relativistic quantum chaos

Liang Huang,Ying-Cheng Lai

Figure 1. Level spacing statistics of the massless Dirac billiards with the boundary being a circle, the Africa shape, the heart shape for left, middle, and right, respectively. The first row shows the unfolded level-spacing distribution P(S), and the second row shows the spectral rigidity Δ3(L). The green dashed–dotted line, cyan dashed line, and blue solid line are for Poisson, GOE, and GUE. Red staircase curves and symbols are numerical results from 13000 energy levels for each shape by diagonalizing the operator $\hat{H}$ given by equation (1). Adapted from [535] with permission.