On a model for rotational tunneling with a $C_{6}$-space-time symetric analog

TL;DR

This paper investigates a simplified model of a rigid rotor with $C_{3}$ symmetry, demonstrating how parity simplifies eigenvalue calculations, and explores a non-Hermitian, space-time-symmetric version revealing real eigenvalues and symmetry-breaking points.

Contribution

It introduces a non-Hermitian space-time-symmetric model related to a $C_{6}$-space-time symmetric analog, extending understanding of eigenvalue behavior in such systems.

Findings

Parity simplifies eigenvalue calculations for the rotor model.

The non-Hermitian model exhibits real eigenvalues under certain conditions.

An exceptional point marks the breaking of antiunitary symmetry.

Abstract

We analyze the simple model of a rigid rotor with $C_{3}$ symmetry and show that the use of parity simplifies considerably the calculation of its eigenvalues. We also consider a non-Hermitian space-time-symmetric counterpart that exhibits real eigenvalues and determine the exceptional point at which the antiunitary symmetry is broken.