Chaos in Jahn-Teller Rattling

TL;DR

This paper reveals chaotic behavior in the energy spectrum of a Jahn-Teller ion in a cubic anharmonic potential, suggesting chaos can be observed in condensed matter experiments like specific heat measurements.

Contribution

It demonstrates the transition from regular to chaotic energy level statistics in an anharmonic Jahn-Teller system, linking chaos to observable condensed matter phenomena.

Findings

Level-spacing distribution transitions from Poisson to Wigner

Chaotic energy scale identified

Potential experimental detection via specific heat

Abstract

We unveil chaotic behavior hidden in the energy spectrum of a Jahn-Teller ion vibrating in a cubic anharmonic potential as a typical model for rattling in cage-structure materials. When we evaluate the nearest-neighbor level-spacing distribution $P(s)$ of eigenenergies of the present oscillator system, we observe the transition of $P(s)$ from the Poisson to the Wigner distribution with the increase of cubic anharmonicity, showing the occurrence of chaos in the anharmonic Jahn-Teller vibration. The energy scale of the chaotic region is specified from the analysis of $P(s)$ and we discuss a possible way to observe chaotic behavior in the experiment of specific heat. It is an intriguing possibility that chaos in nonlinear physics could be detected by a standard experiment in condensed matter physics.