{"title":"非稳态 SQM/IST 对应和线上 CPT/PT 不变的成对哈密顿子","authors":"V P Berezovoj, A J Nurmagambetov","doi":"10.1093/ptep/ptae074","DOIUrl":null,"url":null,"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.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"21 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-stationary SQM/IST correspondence and CPT/PT-invariant paired hamiltonians on the line\",\"authors\":\"V P Berezovoj, A J Nurmagambetov\",\"doi\":\"10.1093/ptep/ptae074\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":20710,\"journal\":{\"name\":\"Progress of Theoretical and Experimental Physics\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Progress of Theoretical and Experimental Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1093/ptep/ptae074\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress of Theoretical and Experimental Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1093/ptep/ptae074","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Non-stationary SQM/IST correspondence and CPT/PT-invariant paired hamiltonians on the line
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.
期刊介绍:
Progress of Theoretical and Experimental Physics (PTEP) is an international journal that publishes articles on theoretical and experimental physics. PTEP is a fully open access, online-only journal published by the Physical Society of Japan.
PTEP is the successor to Progress of Theoretical Physics (PTP), which terminated in December 2012 and merged into PTEP in January 2013.
PTP was founded in 1946 by Hideki Yukawa, the first Japanese Nobel Laureate. PTEP, the successor journal to PTP, has a broader scope than that of PTP covering both theoretical and experimental physics.
PTEP mainly covers areas including particles and fields, nuclear physics, astrophysics and cosmology, beam physics and instrumentation, and general and mathematical physics.