On Faithful Matrix Representations of q-Deformed Models in Quantum Optics
Consider the q-deformed Lie algebra, tq:K^1,K^2q=1−qK^1K^2,K^3,K^1q=sK^3, K^1,K^4q=sK^4,K^3,K^2q=tK^3,K^2,K^4q=tK^4, and K^4,K^3q=rK^1, where r,s,t∈ℝ−0, subject to the physical properties: K^1 and K^2 are real diagonal operators, and K^3=K^4†, († is for Hermitian conjugation). The q-deformed Lie alg...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/6737287 |
| _version_ | 1827000162125348864 |
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| author | Latif A -M. Hanna Abdullah Alazemi Anwar Al-Dhafeeri |
| author_facet | Latif A -M. Hanna Abdullah Alazemi Anwar Al-Dhafeeri |
| author_sort | Latif A -M. Hanna |
| collection | DOAJ |
| description | Consider the q-deformed Lie algebra, tq:K^1,K^2q=1−qK^1K^2,K^3,K^1q=sK^3, K^1,K^4q=sK^4,K^3,K^2q=tK^3,K^2,K^4q=tK^4, and K^4,K^3q=rK^1, where r,s,t∈ℝ−0, subject to the physical properties: K^1 and K^2 are real diagonal operators, and K^3=K^4†, († is for Hermitian conjugation). The q-deformed Lie algebra, tq is introduced as a generalized model of the Tavis–Cummings model (Tavis and Cummings 1968, Bashir and Sebawe Abdalla 1995), namely, K^1,K^2=0,K^1,K^3=−2K^3,K^1,K^4=2K^4,K^2,K^3=K^3,K^2,K^4=K^4, and K^4,K^3=K^1, which is subject to the physical properties K^1 and K^2 are real diagonal operators, and K^3=K^4†. Faithful matrix representations of the least degree of tq are discussed, and conditions are given to guarantee the existence of the faithful representations. |
| first_indexed | 2024-04-11T09:21:01Z |
| format | Article |
| id | doaj.art-0354a48589c34229bf5d4d444ac64c45 |
| institution | Directory Open Access Journal |
| issn | 1687-0425 |
| language | English |
| last_indexed | 2025-02-18T10:40:21Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj.art-0354a48589c34229bf5d4d444ac64c452024-11-02T05:28:18ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/6737287On Faithful Matrix Representations of q-Deformed Models in Quantum OpticsLatif A -M. Hanna0Abdullah Alazemi1Anwar Al-Dhafeeri2Kuwait UniversityKuwait UniversityKuwait UniversityConsider the q-deformed Lie algebra, tq:K^1,K^2q=1−qK^1K^2,K^3,K^1q=sK^3, K^1,K^4q=sK^4,K^3,K^2q=tK^3,K^2,K^4q=tK^4, and K^4,K^3q=rK^1, where r,s,t∈ℝ−0, subject to the physical properties: K^1 and K^2 are real diagonal operators, and K^3=K^4†, († is for Hermitian conjugation). The q-deformed Lie algebra, tq is introduced as a generalized model of the Tavis–Cummings model (Tavis and Cummings 1968, Bashir and Sebawe Abdalla 1995), namely, K^1,K^2=0,K^1,K^3=−2K^3,K^1,K^4=2K^4,K^2,K^3=K^3,K^2,K^4=K^4, and K^4,K^3=K^1, which is subject to the physical properties K^1 and K^2 are real diagonal operators, and K^3=K^4†. Faithful matrix representations of the least degree of tq are discussed, and conditions are given to guarantee the existence of the faithful representations.http://dx.doi.org/10.1155/2022/6737287 |
| spellingShingle | Latif A -M. Hanna Abdullah Alazemi Anwar Al-Dhafeeri On Faithful Matrix Representations of q-Deformed Models in Quantum Optics International Journal of Mathematics and Mathematical Sciences |
| title | On Faithful Matrix Representations of q-Deformed Models in Quantum Optics |
| title_full | On Faithful Matrix Representations of q-Deformed Models in Quantum Optics |
| title_fullStr | On Faithful Matrix Representations of q-Deformed Models in Quantum Optics |
| title_full_unstemmed | On Faithful Matrix Representations of q-Deformed Models in Quantum Optics |
| title_short | On Faithful Matrix Representations of q-Deformed Models in Quantum Optics |
| title_sort | on faithful matrix representations of q deformed models in quantum optics |
| url | http://dx.doi.org/10.1155/2022/6737287 |
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