dorsal/arxiv
View SchemaQuantum Diagonalization Method in the Tavis-Cummings Model
| Authors | Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato, Tatsuo Suzuki, Yukako Wada |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410003 |
| URL | https://arxiv.org/abs/quant-ph/0410003 |
| DOI | 10.1142/S021988780500065X |
| Journal | Int.J.Geom.Meth.Mod.Phys. 2 (2005) 425-440 |
Abstract
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix $A\equiv S_{+}\otimes a+S_{-}\otimes a^{\dagger}$ diagonal to calculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is first nontrivial examples as far as we know, and reproduce the calculations of ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an application to a noncommutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the noncommutativity of operators in quantum physics. Our method may open a new point of view in Mathematical Physics or Quantum Physics.
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"abstract": "To obtain the explicit form of evolution operator in the Tavis-Cummings model\nwe must calculate the term ${e}^{-itg(S_{+}\\otimes a+S_{-}\\otimes\na^{\\dagger})}$ explicitly which is very hard. In this paper we try to make the\nquantum matrix $A\\equiv S_{+}\\otimes a+S_{-}\\otimes a^{\\dagger}$ diagonal to\ncalculate ${e}^{-itgA}$ and, moreover, to know a deep structure of the model.\n For the case of one, two and three atoms we give such a diagonalization which\nis first nontrivial examples as far as we know, and reproduce the calculations\nof ${e}^{-itgA}$ given in quant-ph/0404034. We also give a hint to an\napplication to a noncommutative differential geometry.\n However, a quantum diagonalization is not unique and is affected by some\nambiguity arising from the noncommutativity of operators in quantum physics.\n Our method may open a new point of view in Mathematical Physics or Quantum\nPhysics.",
"arxiv_id": "quant-ph/0410003",
"authors": [
"Kazuyuki Fujii",
"Kyoko Higashida",
"Ryosuke Kato",
"Tatsuo Suzuki",
"Yukako Wada"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1142/S021988780500065X",
"journal_ref": "Int.J.Geom.Meth.Mod.Phys. 2 (2005) 425-440",
"title": "Quantum Diagonalization Method in the Tavis-Cummings Model",
"url": "https://arxiv.org/abs/quant-ph/0410003"
},
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