Quantum chaotic patterns in theE⊗(b1+b2)Jahn-Teller model

Abstract

We study statistical properties of excited levels of the $\mathrm{E}\ensuremath{\bigotimes}({b}_{1}+{b}_{2})$ 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 ($E\ensuremath{\bigotimes}e$ 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 scaling $\ensuremath{\sim}\sqrt{S}$ at small $S$ and resembles the semi-Poisson law $P(S)=4S\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(\ensuremath{-}2S)$ at $S\ensuremath{\ge}1$. The latter is believed to be universal and characteristic, e.g., at the transition between metal and insulator phases.