Quantum chaotic patterns in the E x (b_1+b_2) Jahn-Teller model

TL;DR

This paper investigates the spectral properties of the E x (b_1+b_2) Jahn-Teller model, revealing stable level spacing distributions that differ from Wigner statistics and exhibit semi-Poisson characteristics, indicating complex quantum behavior.

Contribution

It provides the first detailed analysis of level spacing distributions in the E x (b_1+b_2) Jahn-Teller model, highlighting deviations from classical random matrix predictions.

Findings

Level spacing distribution differs from Wigner distribution.

Distribution shows semi-Poisson behavior at larger spacings.

Stable distribution pattern across parameter variations.

Abstract

We study statistical properties of excited levels of the E x (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 x 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 ~$\sqrt{S}$ at small S and resembles the semi-Poisson law P(S)= 4S \exp (-2 S) at S> 1. The latter is believed to be universal and characteristic, e.g., at the transition between metal and insulator phases.