161 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 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
On the Color-Singlet States in Many-Quark Model with the su(4)-Algebraic Structure. II
Ground-state energies are investigated in a many-quark model with pairing
interactions, which has the su(4)-algebraic structure. Exact eigenstates in the
boson realization method are constructed by imposing a color-singlet condition
developed in the previous paper. An interaction term breaking the
su(4)-dynamical symmetry plays an important role to determine the ground state.
As a result, a quark-pairing state or a quark-triplet state as a nucleon is
realized with a certain value of a variable which is regarded as an order
parameter. In addition to the parameter regions in which these ground states
are realized, it is shown that there are two transition regions between the
quark-pairing and the quark-triplet states with different values of the order
parameter.Comment: 19 pages, 12 figures, using PTPTeX clas
A practical scheme for constructing the minimum weight states of the su(n)-Lipkin model in arbitrary fermion number
With the aim of performing an argument supplement to the previous paper by
the present authors, in this paper, a practical scheme for constructing the
minimum weight states of the su(n)-Lipkin model in arbitrary fermion number is
discussed. The idea comes from the following two points : (i) consideration on
the property of one-fermion transfer induced by the su(n)-generators in the
Lipkin model and (ii) use of the auxiliary su(2)-algebra presented by the
present authors. The form obtained under the points (i) and (ii) is simple.Comment: 11 pages, 6 figure
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