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Understanding the Complex Position in a PT-symmetric Oscillator

We study how to understand the complex coordinates involved in the non-Hermitian but PT-symmetric systems. We explore a PT-symmetric oscillator model to show that the entire information on the complex position is attainable. Its real part is from the observation while its imaginary part is from the non-Hermiticity parameter. We also propose a new complex extension of P-transformation and T-transformation (the `parity' and `time reflection' respectively). Particularly, the P-transformation realizes the left-right reflection in the complex plane.

preprint2015arXivOpen access
Jin-Ho Cho
hep-thquant-ph
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Jin-Ho Cho

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