Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149110 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862615306877272064 |
|---|---|
| author | Znojil, M. |
| author_facet | Znojil, M. |
| citation_txt | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Θ ≠ I represented, in Runge-Kutta approximation, by (2R–1)-diagonal matrices.
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| first_indexed | 2025-11-29T13:27:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149110 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-29T13:27:01Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Znojil, M. 2019-02-19T17:27:09Z 2019-02-19T17:27:09Z 2009 Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81U20; 46C15; 81Q10; 34L25; 47A40; 47B50 https://nasplib.isofts.kiev.ua/handle/123456789/149110 One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Θ ≠ I represented, in Runge-Kutta approximation, by (2R–1)-diagonal matrices. This paper is a contribution to the Proceedings of the 5-th Microconference “Analytic and Algebraic Methods V”. The author appreciates the support by the Institutional Research Plan AV0Z10480505, by the MSMT “Doppler Institute” project Nr. LC06002 and by GA ˇ CR grant Nr. 202/07/1307. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators Article published earlier |
| spellingShingle | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators Znojil, M. |
| title | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators |
| title_full | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators |
| title_fullStr | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators |
| title_full_unstemmed | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators |
| title_short | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators |
| title_sort | cryptohermitian picture of scattering using quasilocal metric operators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149110 |
| work_keys_str_mv | AT znojilm cryptohermitianpictureofscatteringusingquasilocalmetricoperators |