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2022•arXiv (Cornell University)Open access

Non-unitary transformation approach to $\mathcal{PT}$ dynamics

Braulio Misael Villegas-Martínez, Francisco Soto‐Eguibar, Sergio A. Hojman, Felipe A. Asenjo, H. M. Moya-Cessa

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Abstract

We show that several Hamiltonians that are $\mathcal{PT}$ symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

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We show that several Hamiltonians that are $\mathcal{PT}$ symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

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Available abstract

We show that several Hamiltonians that are $\mathcal{PT}$ symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

Key concepts: Unitary state, Unitary transformation, Hermitian matrix, Transformation (genetics), Circular ensemble, Mathematical physics, Unitary matrix, Mathematics

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