Perspectives on relativistic quantum chaos

Liang Huang,Ying-Cheng Lai

Figure 2. (a) Chaotic graphene billiard with Africa shape cut from a graphene sheet. The system has 42 505 carbon atoms. The outline is determined by the equation $x+{\rm{i}}{y}=70a$ $(z+0.2{z}^{2}+0.2{z}^{3}{{\rm{e}}}^{{\rm{i}}\pi /3})$, where z is the unit circle in the complex plane, a = 2.46 Å is the lattice constant for graphene. The area is A = 1117 nm2. (b)–(d) are the level spacing distribution, integrated level spacing distribution, and the spectral rigidity, respectively, for 664 energy levels in the range $0.02\lt {E}_{n}/t\lt 0.4$, where t is the hopping energy between nearest neighboring atoms. Dashed line is Poisson, solid line is GOE, and dotted line is GUE. The results show clear evidence of GOE. Adopted from [539] with permission.