Instabilities, nonhermiticity and exceptional points in the cranking model

TL;DR

This paper investigates a cranking harmonic oscillator model used in nuclear and condensate physics, revealing that its apparent hermiticity fails at instability points, which are identified as exceptional points within a PT-symmetric framework.

Contribution

It demonstrates that the model's Hamiltonian is non-hermitian at instability points and connects these to exceptional points in PT-symmetry, providing new insights into the model's spectral properties.

Findings

Instability points correspond to exceptional points.

The Hamiltonian is non-hermitian within the instability region.

The model's PT-symmetry is crucial for understanding its spectral behavior.

Abstract

A cranking harmonic oscillator model, widely used for the physics of fast rotating nuclei and Bose-Einstein condensates, is re-investigated in the context of PT-symmetry. The instability points of the model are identified as exceptional points. It is argued that - even though the Hamiltonian appears hermitian at first glance - it actually is not hermitian within the region of instability.