Quantum chaotic patterns in the E (b1 + b2) Jahn-Teller model

We study statistical properties of excited levels of the E (b(1) + b(2) Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting cases (E e and Holstein model) the distribution of nearest-neighbor spacings is rather stable as to the change of parameters and different from the Wigner one. This limiting distribution assumably shows approximately radical S scaling at small and resembles the semi-Poisson law P(S) = 4S exp(-2S) at S > or = 1. The latter is believed to be universal and characteristic, e.g., at the transition between metal and insulator phases.