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Journal of Physics A Mathematical and General

Description of anharmonic effects with generalized coherent states

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

Published Jan 6, 2004• 2 citations
Publisher

Abstract

The Marumori–Yamamura–Tokunga boson expansion is used to describe multiboson processes. The reliability of the time evolution predicted by generalized coherent states has been investigated numerically by comparing its dynamics with the exact one. A link between the generalized coherent states and deformed bosons is established.
DOI
10.1088/0305-4470/37/3/016

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The Schwinger representation and the Marumori–Yamamura–Tokunaga boson expansion are used to describe the Lipkin model in terms of generalized coherent states. The ground-state energy is obtained within several variant types of coherent states. It has been found that two of the kinds considered describe particularly well the transition from weak to strong coupling, providing a remarkable improvement of the mean-field description of the transition zone. The time evolution predicted by generalized coherent states has been investigated numerically by comparing its dynamics with the exact one.
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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: