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Progress of Theoretical Physics

Investigation of the Minimal Uncertainty Appearing in the Quasi-Spin Coherent and the Quasi-Spin Squeezed State of Many-Fermion System: The Case of Many-Nucleon System in Pairing Correlation

Y. Tsue, A. Kuriyama, M. Yamamura

Published Sep 1, 1994• 0 citations
Publisher

Abstract

Minimal quantal effect in many-nucleon system which is correlated through pairing interaction is investigated in the frame of the quasi-spin coherent and the quasi-spin squeezed state. Basic idea can be found in the case of the su(2)-boson model reported by the present authors. For simplicity, the single-j shell model is adopted. The quasi-spin coherent state, which is well known as the BCS ground-state, shows the minimal uncertainty for quasi-spin operators under a rather restricted condition. In order to relax this restriction, the quasi-spin squeezed state is introduced and it is shown that, with the help of a certain phase angle parameter, the minimal uncertainty for quasi-spin operators can be controlled.

DOI
10.1143/ptp.92.545

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Minimal quantal effect in many-nucleon system which is correlated through pairing interaction is investigated in the frame of the quasi-spin coherent and the quasi-spin squeezed state. Basic idea can be found in the case of the su(2)-boson model reported by the present authors. For simplicity, the single-j shell model is adopted. The quasi-spin coherent state, which is well known as the BCS ground-state, shows the minimal uncertainty for quasi-spin operators under a rather restricted condition. In order to relax this restriction, the quasi-spin squeezed state is introduced and it is shown that, with the help of a certain phase angle parameter, the minimal uncertainty for quasi-spin operators can be controlled.
A viewpoint for describing time development of wave packet with the least quantal effect is proposed in the case of system obeying the su(2)-algebra, i.e., the quasi-spin. The basic idea is a possible extension of a method developed by the present authors, together with Tsue and Fujiwara, for one-dimensional system. Concerning the least quantal effect, the uncertainty relations coming from the non-commutability among the components of the quasi-spin are investigated and a certain condition for the least quantal effect in the quasi-spin is presented.
To go beyond the usual Hartree-Fock approximation, a quasi-spin squeezed state is introduced in the Lipkin model. We define the quasi-spin squeezed state from the su(2)-coherent state in a manner similar to that for the ordinary boson squeezed state. In this paper, we deal only with the case that the parameters included in this state are time-independent. It is then seen that the exact energy eigenvalues of the ground state are reproduced with high accuracy in all regions of the force strength χ by using the quasi-spin squeezed state. Also, it is shown that the quasi-spin squeezed state gives a classical counterpart with a certain correction for the Holstein-Primakoff boson representation of su(2)-spin. We investigate uncertainty relations for su(2)-generators and the meaning of “squeezing” is clarified.
A viewpoint for describing time development of wave packet with the least quantal effect is proposed in the case of system obeying the su(2)-algebra, i.e., the quasi-spin. The basic idea is a possible extension of a method developed by the present authors, together with Tsue and Fujiwara, for one-dimensional system. Concerning the least quantal effect, the uncertainty relations coming from the non-commutability among the components of the quasi-spin are investigated and a certain condition for the least quantal effect in the quasi-spin is presented.