Non-stationary SQM/IST Correspondence and ${\cal CPT}/{\cal PT}$-invariant paired Hamiltonians on the line

• URL: http://arxiv.org/abs/2402.19066v3
• Date: Sat, 11 May 2024 17:27:29 GMT
• Title: Non-stationary SQM/IST Correspondence and ${\cal CPT}/{\cal PT}$-invariant paired Hamiltonians on the line
• Authors: V. P. Berezovoj, A. J. Nurmagambetov,
• Abstract summary: We extend the consideration to the case of paired stationary and non-stationary Hamiltonians. We find the way of constructing non-hermitian Hamiltonians from the initially hermitian ones. The relevance of our proposal to Quantum Optics and optical waveguides technology, as well as to non-valued dynamics and Black Hole Physics is briefly discussed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We fill some of existed gaps in the correspondence between Supersymmetric Quantum Mechanics and the Inverse Scattering Transform by extending the consideration to the case of paired stationary and non-stationary Hamiltonians. We formulate the corresponding to the case Goursat problem and explicitly construct the kernel of the non-local Inverse Scattering Transform, which solves it. As a result, we find the way of constructing non-hermitian Hamiltonians from the initially hermitian ones, that leads, in the case of real-valued spectra of both potentials, to pairing of ${\cal CPT/PT}$-invariant Hamiltonians. The relevance of our proposal to Quantum Optics and optical waveguides technology, as well as to non-linear dynamics and Black Hole Physics is briefly discussed.

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