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Manifestation of superposition and coherence in ${\mathcal P} {\mathcal T}$ -symmetry through the η-inner product

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… Click to show full 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.

Keywords: superposition coherence; cal symmetric; inner product; superposition

Journal Title: Journal of Physics A: Mathematical and Theoretical
Year Published: 2018

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