arXiv subjects

Y. Tsue

Publications and source records attributed to Y. Tsue.

At least 55 records · Page 3Linked to original sources

arXiv2007

Landau Potential Study of the Chiral Phase Transition in a QCD-Like Theory

We investigate the chiral phase transition of a QCD-like theory, based the shape change of the effective potential near the critical point. The potential is constructed with the auxiliary field method, and a source term coupled to the field is introduced in order to compute the potential shape numerically. We also generalize the potential so as to have two independent order parameters, the quark scalar density and the number density. We find a tri-critical point locating at (T,mu)=(97, 203) MeV, and visualize it as the merging point of three potential minima.

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arXiv2007

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 $su(2)\otimes su(2)$-coherent state, which may be natural selection for the two-level pairing model governed by the $su(2)\otimes su(2)$-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 $su(2)\otimes su(1,1)$- and the $su(1,1)\otimes su(1,1)$-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.

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arXiv2007

A Refined Numerical Result on the First Excitation Energy in the Two-Level Pairing Model

The first excitation energy in the two-level pairing model is investigated in terms of the equilibrium and the small fluctuation around it. The basic idea is an extension of results presented in a previous paper by the present authors. In this investigation, the result obtained in the previous paper plays a central role: At the limit of the weak and the strong interaction strength, the results are in good agreement with the exact one. The former and the latter are calculated in the framework of the $su(2)\otimes su(1,1)$- and the $su(2)\otimes su(2)$-coherent state, respectively. On the basis of the above conclusion, the intermediate region for the interaction strength is described in terms of the idea of the interpolation and it is shown that the agreement of the result with the exact one is quite good.

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arXiv2006

Semi-Classical Approach to the Two-Level Pairing Model --Various Aspects of Phase Change--

Aspects of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approch with the mixed-mode coherent state. In the classical limit, $hbar \to 0$, the sharp phase transition appears and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the above-mentioned behavior of the phase change disappears in the analytical and the numerical treatments. As a result, new understanding about aspects of the phase change in this model is given.

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arXiv2006

Effects of mode-mode and isospin-isospin correlations on domain formation of disoriented chiral condensates

The effects of mode-mode and isospin-isospin correlations on nonequilibrium chiral dynamics are investigated by using the method of the time dependent variational approach with squeezed states as trial states. Our numerical simulations show that large domains of the disoriented chiral condensate (DCC) are formed due to the combined effect of the mode-mode and isospin-isospin correlations. Moreover, it is found that, when the mode-mode correlation is included, the DCC domain formation is accompanied by the amplification of the quantum fluctuation, which implies the squeezing of the state. However, neither the DCC domain formation nor the amplification of the quantum fluctuation is observed if only the isospin-isospin correlation is included. This suggests that the mode-mode coupling plays a key role in the DCC domain formation.

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arXiv2006

The Lipkin Model in Many-Fermion System as an Example of the su(1,1) times su(1,1)-Algebraic Model

Following the idea, recently, proposed by the present authors for the two-level pairing model, the Lipkin model is reexamined. It is a natural generalization of the method already developed by the present authors with Kuriyama. This model is a schematic model for many-fermion system and obeys the su(2)-algebra. It is shown that the use of the Schwinger boson representation, the model is expressed in terms of the su(1,1) times su(1,1)-algebra and with the aid of the MYT mapping method, it is disguised from the orginal form in terms of the Holstein-Primakoff representation. Further, under various coherent states, the classical counterparts are derived. It is concluded that the Lipkin model can be treated in the common ring as that of the two-level pairing model.

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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

Effective Potential Study of the Chiral Phase Transition in a QCD-like Theory

We construct the effective potential for a QCD-like theory using the auxiliary field method. The chiral phase transition exhibited by the model at finite temperature and the quark chemical potential is studied from the viewpoint of the shape change of the potential near the critical point. We further generalize the effective potential so as to have quark number and scalar quark densities as independent variables near the tri-critical point.

hep-ph↗

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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arXiv2005

Note on the Time Dependent Variational Approach with Quasi-Spin Squeezed State for Pairing Model

A simple many-fermion system in which there exists N identical fermions in a single spherical orbit with pairing interaction is treated by means of the time-dependent variational approach with a quasi-spin squeezed state with the aim of going beyond the time-dependent Hartree-Fock or Bogoliubov theory. It is shown that the ground state energy is reproduced well analytically in this approach.

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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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