理论物理通讯：英文版

Two-Mode Wigner Operator in 〈ξ| Representation and 〈γ| Representation

Song, Tong-Qiang, Fan, Hong-Yi

Published Jan 1, 2001• 0 citations

Abstract

We derive the two-mode Wigner operator in the 〈ξ| representation and 〈γ| representation, where |ξ〉 is common eigenvector of the mass-weighted relative coordinate and the mass-combinatorial momentum. As an application,we calculate the Wigner function of some two-mode state.

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理论物理通讯：英文版

Two-Mode Wigner Operator in 〈ξ| Representation and 〈γ| Representation

Song, Tong-Qiang, Fan, Hong-Yi

Published Jan 1, 2001• 0 citations

OpenAlex

Abstract

Related papers

Two-Mode Wigner Operator in 〈ξ| Representation and 〈τ| Representation

Song Tong-Qiang, Fan Hong-Yi

Communications in Theoretical PhysicsDec 15, 20010 citations

Two-Mode Wigner Operator in <η| Representation

Wu He-jun, Hong-Yi Fan

Modern Physics Letters BJun 10, 199720 citations

WEYL CORRESPONDENCE AND PATH INTEGRAL FOR TWO-MODE CORRELATED SYSTEM

Hong-Yi Fan, Yue Fan

Modern Physics Letters AFeb 28, 199826 citations

New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application

Shi-Min Xu, Xing-Lei Xu, Hongqi Li +1 more

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix |ξ 1 , ξ 2 〉 C,D C,D 〈ξ 1 , ξ 2 | is a Radon transform of Wigner operator.We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix |ξ 1 , ξ 2 〉 C,D C,D 〈ξ 1 , ξ 2 | is a Radon transform of Wigner operator.

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Fan Hong-Yi, Ye Xiong

We give the explicit form of the common eigenstate \ensuremath{\Vert}\ensuremath{\xi}〉 of the center-of-mass coordinate ${\mathrm{\ensuremath{\mu}}}_{1}$ ${\mathit{Q}}_{1}$ +${\mathrm{\ensuremath{\mu}}}_{2}$ ${\mathit{Q}}_{2}$ and the mass-weighted relative momentum ${\mathrm{\ensuremath{\mu}}}_{2}$ ${\mathit{P}}_{1}$ -${\mathrm{\ensuremath{\mu}}}_{1}$ ${\mathit{P}}_{2}$ of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators ${\mathit{Q}}_{2}$ - ${\mathit{Q}}_{1}$ and ${\mathit{P}}_{1}$ + ${\mathit{P}}_{2}$ . The orthonormal and completeness relation of \ensuremath{\Vert}\ensuremath{\xi}〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for ${\mathrm{\ensuremath{\mu}}}_{1}$ ${\mathit{Q}}_{1}$ +${\mathrm{\ensuremath{\mu}}}_{2}$ ${\mathit{Q}}_{2}$ and ${\mathrm{\ensuremath{\mu}}}_{2}$ ${\mathit{P}}_{1}$ -${\mathrm{\ensuremath{\mu}}}_{1}$ ${\mathit{P}}_{2}$ is also derived by using the \ensuremath{\Vert}\ensuremath{\xi}〉 representation.We give the explicit form of the common eigenstate \ensuremath{\Vert}\ensuremath{\xi}〉 of the center-of-mass coordinate ${\mathrm{\ensuremath{\mu}}}_{1}$${\mathit{Q}}_{1}$+${\mathrm{\ensuremath{\mu}}}_{2}$${\mathit{Q}}_{2}$ and the mass-weighted relative momentum ${\mathrm{\ensuremath{\mu}}}_{2}$${\mathit{P}}_{1}$-${\mathrm{\ensuremath{\mu}}}_{1}$${\mathit{P}}_{2}$ of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators ${\mathit{Q}}_{2}$-${\mathit{Q}}_{1}$ and ${\mathit{P}}_{1}$+${\mathit{P}}_{2}$. The orthonormal and completeness relation of \ensuremath{\Vert}\ensuremath{\xi}〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for ${\mathrm{\ensuremath{\mu}}}_{1}$${\mathit{Q}}_{1}$+${\mathrm{\ensuremath{\mu}}}_{2}$${\mathit{Q}}_{2}$ and ${\mathrm{\ensuremath{\mu}}}_{2}$${\mathit{P}}_{1}$-${\mathrm{\ensuremath{\mu}}}_{1}$${\mathit{P}}_{2}$ is also derived by using the \ensuremath{\Vert}\ensuremath{\xi}〉 representation.

Physical Review AApr 1, 1995124 citations

We give the explicit form of the common eigenstate \ensuremath{\Vert}\ensuremath{\xi}〉 of the center-of-mass coordinate ${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{Q}}_{1}

+${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{Q}}_{2}

and the mass-weighted relative momentum ${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{P}}_{1}

-${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{P}}_{2}

of two particles, which is more complicated than the common eigenstate of the other pair of commutative operators

{\mathit{Q}}_{2}

{\mathit{Q}}_{1}

and

{\mathit{P}}_{1}

{\mathit{P}}_{2}

. The orthonormal and completeness relation of \ensuremath{\Vert}\ensuremath{\xi}〉 are investigated easily by virtue of the technique of integration within an ordered product of operators. The normally ordered squeezing operator for ${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{Q}}_{1}

+${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{Q}}_{2}

and ${\mathrm{\ensuremath{\mu}}}_{2}$

{\mathit{P}}_{1}

-${\mathrm{\ensuremath{\mu}}}_{1}$

{\mathit{P}}_{2}

is also derived by using the \ensuremath{\Vert}\ensuremath{\xi}〉 representation.