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Various classical counterparts for the two-level pairing model in amany-fermion system are presented in the Schwinger boson representation. It isshown that one of the key ingredients giving the classical descriptions forquantal system is the use of the various trial states besides the $su(2)\otimessu(2)$-coherent state, which may be natural selection for the two-level pairingmodel governed by the $su(2)\otimes su(2)$-algebra. It is pointed out that thefictitious behavior like the sharp phase transition can be avoided by using theother states such as the $su(2)\otimes su(1,1)$- and the $su(1,1)\otimessu(1,1)$-coherent states, while the sharp phase transition appears in the usualHartree-Fock-Bogoliubov and the quasi-particle random phase approximations inthe original fermion system.Comment: 19 pages, 5 figures, using PTPTeX.cl

Classical and Quantal Descriptions of Small Amplitude Fluctuations around Equilibriums in the Two-Level Pairing Model