Manifestation of Superposition and Coherence in $\cal PT$-symmetry through the $\eta$-inner Product

TL;DR

This paper explores how $ m PT$-symmetric quantum systems exhibit unique superposition and coherence properties using the $ m exteta$-inner product, providing insights into their physical interpretation and differences between broken and unbroken phases.

Contribution

It introduces a novel analysis of $ m PT$-symmetric quantum mechanics via the $ m exteta$-inner product, linking superposition, coherence, and physical interpretation in $ ext C^2$.

Findings

$ m PT$-symmetric systems have stationary superposition properties

The $ m exteta$-inner product distinguishes broken and unbroken phases

Physical interpretation via Stokes parameters clarifies system behavior

Abstract

Through the $\eta$-inner product, we investigate $\cal PT$-symmetric quantum mechanics from the viewpoint of superposition and coherence theory. It is argued that $\cal PT$-symmetric quantum systems are endowed with stationary superposition or superposition-free properties. A physical interpretation of $\eta$-inner product in $\mathbb C^2$ is given through the Stokes parameters, showing the difference between broken and unbroken $\cal PT$-symmetric quantum systems.