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M. Yamamura

Publications and source records attributed to M. Yamamura.

At least 55 records · Page 3Linked to original sources
arXiv2006

A New Boson Realization of Two-Level Pairing Model in Many-Fermion System and its Classical Counterpart

A new method for describing the two-level pairing model in a many-fermion system is presented. Basic idea comes from the Schwinger boson representation for the su(2) cross su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the mixed-mode coherent state is mainly discussed in this paper.

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arXiv2006

A Note on the Two-Level Pairing Model Obeying the su(2)*su(2)-Algebra

The two-level pairing model obeying the su(2)*su(2)-algebra, which was discussed in the previous paper, is re-formed in the framework of the su(1,1)*su(1,1)-algebra in the Schwinger boson representation. With the aid of MYT mapping method, the Schwinger boson representation is reduced to the Holstein-Primakoff boson representation, which is expressed in terms of two kinds of bosons. Further, with the aid of the squeezed coherent state, the classical counterpart is obtained.

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arXiv2005

Boson Realization of the su(3)-Algebra. IV

On the basis of the Schwinger boson representation for the Elliott model developed in (III), the Holstein-Primakoff representation for the su(3)-algebra is presented. The basic idea is the same as that adopted in (II), and as an example, the case of the lowest approximation is shown.

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arXiv2005

Boson Realization of the su(3)-Algebra. III

Following the basic idea developed in (I), the su(3)-model presented by Elliott is investigated. A method for constructing the orthogonal set, in which the angular momenta are good quantum numbers, is discussed without using the angular momentum projection.

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arXiv2005

Boson Realization of the su(3)-Algebra. I

Following a general form for the Schwinger boson representation of the su(M+1) Lipkin model presented in the previous paper, three types of the orthogonal sets characterizing the su(3)-algebra are proposed. In these three, third is presented in Appendix. The intrinsic state is specified by two quantum numbers and two excited state generating operators play a central role.

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arXiv2005

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.

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arXiv2005

The Lipkin Model in the su(M+1)-Algebra for Many-Fermion System and its Counterpart in the Schwinger Boson Representation

Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators such as the particle-hole pairs are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and the su(4)-algebra are discussed. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high temperature superconductivity.

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arXiv2005

On Parametric Resonance in Quantum Many-Body System

The dynamics governed by a requantized collective Hamiltonian in the coupled Lipkin model is investigated in the time-dependent variational approach with squeezed state. It is pointed out that there is a possibility of the parametric resonance mechanism which leads to amplifying the amplitude of quantum fluctuation around the collective mode in this model.

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arXiv2004

On the Eigenvalue Problem of the su(1,1)-Algebra and the Coupling Scheme of Two su(1,1)-Spins

After recapitulating the eigenvalue problem of the su(1,1)-algebra in the conventional form, the same problem is treated in an unconventional form, in which the eigenvalue is pure imaginary. Further, the coupling scheme of two su(1,1)-spins is discussed in the framework of two possibilities, in which certain new aspects appear. Finally, the coupling scheme developed in this paper is applied to a concrete example, which will serve boson realization of the so(4)- and the so(3,1)-algebra presented in the next paper.

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arXiv2004

A Note on the Eigenvalue Problem in the su(1,1)-Algebra

Normalization constant in the eigenstate appearing in the eigenvalue problem of the su(1,1)-algebra is discussed. This normalization constant is expressed in terms of the Gauss' hypergeometric series which is not absolutely convergent. It is proved that this series is obtained as a certain limit of an absolutely convergent series, which was conjectured in the previous paper.

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arXiv2004

A Possible Boson Realization of the so(4)- and the so(3,1)-Algebra

As natural extensions of the boson realizations of the su(2)- and the su(1,1)-algebra, the so(4)- and the so(3,1)-algebras are presented in the form of boson realizations with four kinds of boson operators. For each algebra, two forms are discussed. One is constructed in terms of two sets of the boson operators which play a role of spherical tensor with rank 1/2. The other is based on the ranks 1 and 0. As a possible application, the Runge-Lenz-Pauli vector, which is famous in the hydrogen atom, is derived with some aspects.

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arXiv2004

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.

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arXiv2004

Deformed Boson Scheme Stressing Even-Odd Boson Number Difference. III

A basic idea is proposed for extending the formalism of Part (II) of the series of our paper to the case of the parameter-dependent deformation. It is stressed that, through this extension, the variety of the application increases. Further, an answer for the problem mentioned in Part (II) is presented.

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arXiv2003

Deformed Boson Scheme Stressing Even-Odd Boson Number Difference. II

The boson-pair coherent state developed in Part (I) is generalized to the case in which the state is a mixture of even-boson and odd-boson number states. A general framework is shown and its three concrete examples are discussed. Main idea is in the application of the deformed boson scheme presented by the present authors.

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arXiv2003

Deformed Boson Scheme Stressing Even-Odd Boson Number Difference. I

An idea of the deformed boson scheme developed by the present authors is applied to the case of boson-pair coherent state. In this state, even and odd boson number difference is stressed and various concrete examples of the boson-pair coherent states are shown. Concerning some of them, mutual relations are investigated in connection to the su(1,1)-algebra. A formulation in terms of the MYT boson mapping is also performed.

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arXiv2003

Note on the Orthogonal Set in Six Kinds of Boson Operators --In Relation to the su(1,1)- and its Relevant Algebras--

Following the basic idea proposed by the present authors in recent paper, a possible form of the orthogonal set for many-body system consisting of six kinds of boson operators is developed. In contrast to the recent paper, in which the su(2)-algebra plays a central role, in this paper, the su(1,1)-algebra is in a central position. The orthogonal set obtained in this paper is expressed in terms of monomial with respect to the state generating operators.

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arXiv2003

On the Boson Number Operator in the Deformed Boson Scheme

Concerning the energy of harmonic oscillator, a prescription is proposed for making the original form unchanged even after q-deformation. Applicability of the prescription is limited, but, it can be applied to various cases which are well known.

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