Chaos and its quantization in dynamical Jahn-Teller systems

TL;DR

This paper explores quantum chaos in Jahn-Teller systems by analyzing how anharmonicity induces chaos, affecting electronic properties and magnetic responses in crystal systems.

Contribution

It demonstrates the transition from regular to chaotic behavior in Jahn-Teller systems due to anharmonicity and studies its impact on electronic and magnetic properties.

Findings

Transition from Poisson to Wigner level statistics with increasing anharmonicity

Chaoticity causes irregular oscillations in the magnetic g-factor

Anharmonic potential induces nonintegrability and chaos in the system

Abstract

We investigate the $E_g \otimes e_g$ Jahn-Teller system for the purpose to reveal the nature of quantum chaos in crystals. This system simulates the interaction between the nuclear vibrational modes and the electronic motion in non-Kramers doublets for multiplets of transition-metal ions. Inclusion of the anharmonic potential due to the trigonal symmetry in crystals makes the system nonintegrable and chaotic. Besides the quantal analysis of the transition from Poisson to Wigner level statistics with increasing the strength of anharmonicity, we study the effect of chaos on the electronic orbital angular momentum and explore the magnetic $g$-factor as a function of the system's energy. The regular oscillation of this factor changes to a rapidly-decaying irregular oscillation by increasing the anharmonicity (chaoticity).