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

Autor:	Berezovoj, V. P., Nurmagambetov, A. J.
Rok vydání:	2024
Předmět:	High Energy Physics - Theory Quantum Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages; v.2: typos fixed, minor changes; v.3 minor changes, Appendix added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.19066 Zobrazit plný text záznamu View this record from Arxiv