Non-Hermitian PT-symmetric and Hermitian Hamiltonians' correspondence: Isospectrality and mass signature

TL;DR

This paper explores how certain transformations relate non-Hermitian PT-symmetric Hamiltonians to Hermitian ones, demonstrating their spectral equivalence and implications for mass signatures in quantum systems.

Contribution

It introduces a transformation framework that connects PT-symmetric and Hermitian Hamiltonians, highlighting their isospectrality and effects on mass signatures.

Findings

Transformations can convert PT-symmetric Hamiltonians into Hermitian counterparts.

PT-symmetric and Hermitian Hamiltonians can be isospectral under these transformations.

The mass signature of Hamiltonians is affected by the transformation process.

Abstract

A transformation of the form x to iy; x,y in R, or an equivalent similarity transformation with a metric operator $\eta$ are shown to transform non-Hermitian PT-symmetric Hamiltonians into Hermitian partner Hamiltonians in Hilbert space. Isospectrality and mass signature are discussed.