### Abstract

To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term e^{-itg(S+⊗a+S-⊗a†)} explicitly which is very hard. In this paper we try to make the quantum matrix A ≡ S_{+}⊗a+S_{-}⊗a^{†} 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 the 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 non-commutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the non-commutativity of operators in quantum physics. Our method may open a new point of view in mathematical or quantum physics.

Original language | English |
---|---|

Pages (from-to) | 425-440 |

Number of pages | 16 |

Journal | International Journal of Geometric Methods in Modern Physics |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Jun |

Externally published | Yes |

### Fingerprint

### Keywords

- Evolution operator
- Non-commutativity
- Quantum diagonalization
- Tavis-Cummings model

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*International Journal of Geometric Methods in Modern Physics*,

*2*(3), 425-440. https://doi.org/10.1142/S021988780500065X

**Quantum diagonalization method in the Tavis-Commings model.** / Fujii, Kazuyuki; Higashida, Kyoko; Kato, Ryosuke; Suzuki, Tatsuo; Wada, Yukako.

Research output: Contribution to journal › Article

*International Journal of Geometric Methods in Modern Physics*, vol. 2, no. 3, pp. 425-440. https://doi.org/10.1142/S021988780500065X

}

TY - JOUR

T1 - Quantum diagonalization method in the Tavis-Commings model

AU - Fujii, Kazuyuki

AU - Higashida, Kyoko

AU - Kato, Ryosuke

AU - Suzuki, Tatsuo

AU - Wada, Yukako

PY - 2005/6

Y1 - 2005/6

N2 - To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term e-itg(S+⊗a+S-⊗a†) explicitly which is very hard. In this paper we try to make the quantum matrix A ≡ S+⊗a+S-⊗a† 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 the 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 non-commutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the non-commutativity of operators in quantum physics. Our method may open a new point of view in mathematical or quantum physics.

AB - To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term e-itg(S+⊗a+S-⊗a†) explicitly which is very hard. In this paper we try to make the quantum matrix A ≡ S+⊗a+S-⊗a† 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 the 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 non-commutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the non-commutativity of operators in quantum physics. Our method may open a new point of view in mathematical or quantum physics.

KW - Evolution operator

KW - Non-commutativity

KW - Quantum diagonalization

KW - Tavis-Cummings model

UR - http://www.scopus.com/inward/record.url?scp=33746288346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746288346&partnerID=8YFLogxK

U2 - 10.1142/S021988780500065X

DO - 10.1142/S021988780500065X

M3 - Article

VL - 2

SP - 425

EP - 440

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 3

ER -