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

Various classical counterparts to the two-level pairing model in a many-fermion system are presented in the Schwinger boson representation. It is shown that one of the key ingredients giving the classical descriptions for quantal systems is the use of various trial states in addition to the su(2) [○!×] su(2)-coherent state, which may be a natural selection for the two-level pairing model governed by the su(2) [○!×] su(2)-algebra. It is pointed out that a spurious behavior such as a sharp phase transition can be avoided by using the other states including the su(2) [○!×] su(1, 1)- and su(1, 1) [○!×] su(1, 1)-coherent states. This contrasts with the situation regarding the usual Hartree-Fock-Bogoliubov and quasi-particle random phase approximations applied to the original fermion system, which yield a sharp phase transition.