209 research outputs found
Coupling Schemes for an n su(2) Spin System
In the framework of the Schwinger boson representation for the su(2)-algebra,
the closed form is derived for the total spin eigenstates which result from the
coupling of n su(2)-spins. In order to demonstrate its usefulness, the
orthogonal set for the so(5)-algebra, which is reduced to four su(2)-spin
systems, is obtained.Comment: 19 pages, no figur
Boson Realization of the su(3)-Algebra. II
On the basis of the Schwinger boson representation for the Lipkin model
developed in (I), the Holstein-Primakoff representation for the su(3)-algebra
is presented. Including the symmetric case, the representation obtained in this
paper contains all the cases.Comment: 12 pages, no figure, using PTP.cl
Classical and Quantal Descriptions of Small Amplitude Fluctuations Around Equilibriums in the Two-Level Pairing Model
Various classical counterparts for 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 system is the use of the various trial states besides the -coherent state, which may be natural selection for the two-level pairing
model governed by the -algebra. It is pointed out that the
fictitious behavior like the sharp phase transition can be avoided by using the
other states such as the - and the -coherent states, while the sharp phase transition appears in the usual
Hartree-Fock-Bogoliubov and the quasi-particle random phase approximations in
the original fermion system.Comment: 19 pages, 5 figures, using PTPTeX.cl
A possible framework of the Lipkin model obeying the su(n)-algebra in arbitrary fermion number. II --- Two subalgebras in the su(n)-Lipkin model and an approach to the construction of linearly independent basis ---
Standing on the results for the minimum weight states obtained in the
previous paper (I), an idea how to construct the linearly independent basis is
proposed for the su(n)-Lipkin model. This idea starts in setting up m
independent su(2)-subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,...).
The original representation is re-formed in terms of the spherical tensors for
the su(n)-generators built under the su(2)-subalgebras. Through this
re-formation, the su(m)-subalgebra can be found. For constructing the linearly
independent basis, not only the su(2)-algebras but also the su(m)-subalgebra
play a central role. Some concrete results in the cases with n=2, 3, 4 and 5
are presented.Comment: 25 pages, 1 figur
A Pseudo su(1,1)-Algebraic Deformation of the Cooper-Pair in the su(2)-Algebraic Many-Fermion Model
A pseudo su(1,1)-algebra is formulated as a possible deformation of the
Cooper-pair in the su(2)-algebraic many-fermion system. With the aid of this
algebra, it is possible to describe behavior of individual fermions which are
generated as the result of interaction with the external environment. The form
presented in this paper is a generalization of a certain simple case developed
recently by the present authors. Basic idea follows the su(1,1)-algebra in the
Schwinger boson representation for treating energy transfer between the
harmonic oscillator and the external environment. Hamiltonian is given under
the idea of the phase space doubling in the thermo-field dynamics formalism and
the time-dependent variational method is applied to this Hamiltonian. Its trial
state is constructed in the frame deformed from the BCS-Bogoliubov approach to
the superconductivity. Several numerical results are shown.Comment: 49 pages, 13 figures, using PTPTEX.cl
Beyond the Schwinger boson representation of the su(2)-algebra. I -- New boson representation based on the su(1,1)-algebra and its related problems with application
With the use of two kinds of boson operators, a new boson representation of
the su(2)-algebra is proposed. The basic idea comes from the pseudo
su(1,1)-algebra recently given by the present authors. It forms a striking
contrast to the Schwinger boson representation of the su(2)-algebra which is
also based on two kinds of bosons. This representation may be suitable for
describing time-dependence of the system interacting with the external
environment in the framework of the thermo field dynamics formalism, i.e., the
phase space doubling. Further, several deformations related to the
su(2)-algebra in this boson representation are discussed. On the basis of these
deformed algebra, various types of time-evolution of a simple boson system are
investigated.Comment: 31 pages, 6 figure
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