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arXiv:nucl-th/0106033 · Progress of Theoretical Physics

Deformed Boson Scheme including Conventional q-Deformation in Time-Dependent Variational Method. I: The Case of Many-Body Systems Consisting of One Kind of Boson Operator

A. Kuriyama, Constança Providência, João da Providência, Y. Tsue, M. Yamamura

Published Oct 1, 2001• 5 citations
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Abstract

Various aspects of the deformed boson scheme are investigated with the aim of applying it to the time-dependent variational method for many-boson systems. The case of the multiboson states is also discussed. In analogy with the time-dependent Hartree-Fock theory in many-fermion systems, the classical aspect of the deformed boson is discussed.

DOI
10.1143/ptp.106.751

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Progress of Theoretical Physics•Aug 1, 2002•0 citations
Various aspects of the deformed boson scheme are investigated with the aim of applying it to the time-dependent variational method for many-boson systems. The case of the multiboson states is also discussed. In analogy with the time-dependent Hartree-Fock theory in many-fermion systems, the classical aspect of the deformed boson is discussed.
Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent state given by the present authors is generalized and the su(2)_q- and the su(1,1)_q-algebras are obtained in the form expressed in terms of four kinds of boson operators. As an illustrative example of the application, the framework for describing thermal effects observed in two-level shell model under the pairing correlation is proposed.
The treatment for the multiboson coherent state is extended for the completeness of the formulation. The basic idea for the extension is presented in terms of expanding the boson space. The MYT boson mapping plays a central role. The resultant multiboson coherent state includes the state obtained in our previous treatment and the form suggests various multiboson coherent states are possible in the deformed boson scheme. 1 typeset using PTPTEX.sty <ver.1.0>Recently, the present authors published four papers 1), 2), 3) concerning the deformed boson scheme including conventional q-deformation in time-dependent variational method. The series of these papers consists of (I), 1) (II), 2) (III) 2) and the short note 3) and, in this series, we discussed various aspects of the q-deformation appearing in the boson coherent state and its generalized form. For example, in (I), 1) a possible form of the multiboson coherent state and its generalization were described. Its treatment is, in some sense, in close connection with that given by Penson and Solomon. 4) However, the treatment in (I) is limited to a certain special boson subspace. In this sense, it is unsatisfactory and to make it complete is the aim of this paper. Further, the present paper gives a generalization of the treatment proposed by the present authors, which is related to a new boson realization in the Lipkin 5), 6) model. In (I), a possible form of the multiboson coherent state, which we denote as |c0〉〉, was defined in the boson space ˜ B composed by the boson operator (˜c, ˜c ∗ ) in the following form:
Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent state given by the present authors is generalized and the su(2)_q- and the su(1,1)_q-algebras are obtained in the form expressed in terms of four kinds of boson operators. As an illustrative example of the application, the framework for describing thermal effects observed in two-level shell model under the pairing correlation is proposed.
The basic idea presented in Parts (I) – (III) of this series for the deformed boson scheme is applied to the case of the su(2)- and the su(1, 1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent state given by the present authors is generalized and the su(2)q- and the su(1, 1)q-algebras are obtained in forms expressed in terms of four kinds of boson operators. As an illustrative example demonstrating the application of the deformed boson scheme, the framework for describing thermal effects observed in the two-level shell model with pairing correlation is proposed.