Spectral Statistics of the Triaxial Rigid Rotator: Semiclassical Origin of their Pathological Behavior

TL;DR

This paper explores the spectral properties of the triaxial rigid rotator, revealing that its energy levels exhibit anomalous statistics similar to a one-dimensional harmonic oscillator, with implications for understanding its classical and quantum behavior.

Contribution

The study uncovers the semiclassical origin of the pathological spectral statistics in the triaxial rigid rotator, combining diagonalization, semiclassical, and algebraic methods.

Findings

Energy spectrum divided into librational and rotational levels.

Spectral statistics follow those of a one-dimensional harmonic oscillator.

Classical analogs correspond to distinct motion types.

Abstract

In this paper we investigate the local and global spectral properties of the triaxial rigid rotator. We demonstrate that, for a fixed value of the total angular momentum, the energy spectrum can be divided into two sets of energy levels, whose classical analog are librational and rotational motions. By using diagonalization, semiclassical and algebric methods, we show that the energy levels follow the anomalous spectral statistics of the one-dimensional harmonic oscillator.