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J. da Providencia

Publications and source records attributed to J. da Providencia.

At least 37 records · Page 2Linked to original sources
arXiv2012

The BCS-Bogoliubov and the su(2)-Algebraic Approach to the Pairing Model in Many-Fermion System

The relation between two approaches to the su(2)-algebraic many-fermion model is discussed: (1) the BCS-Bogoliubov approach in terms of the use of the quasiparticles representing all the degrees of freedom except those related to the Cooper-pairs and (2) the conventional algebraic approach in terms of the use of the minimum weight states, from which the Cooper-pairs are excluded. In order to arrive at the goal, the idea of the quasiparticles is brought up in the conservation of the fermion number. Under the c-number replacement for the three su(2)-generators, the quasiparticles suggested in this paper are reduced to those in the BCS-Bogoliubov approach. It is also shown that the two approaches are equivalent through the c-number replacement. Further, a certain modification of the BCS-Bogoliubov approach is discussed.

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arXiv2012

A Role of the Quasiparticle in the Conservation of the Fermion Number

The role of the "quasiparticle" introduced in last paper by the present authors is discussed. It serves as a guide for the deformation of the Cooper-pair in the BCS-Bogoliubov approach. As an illustrative example, a certain case is treated. This case produces the su(1,1)-like behavior in the su(2)-algebraic many-fermion system.

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arXiv2012

Color-Singlet Three-Quark States in the su(4)-Algebraic Many-Quark Model

As announced in last paper by the present authors, the color-singlet three-quark states are investigated for the case of the spherical j-j coupling and L-S coupling shell models. The latter case automatically leads to the su(4)*su(4)-model. For a certain type of Hamiltonian, the states of individual "nucleons" are characterized.

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arXiv2011

Note on the Minimum Weight States in the su(2)-Algebraic Many-Fermion Model --- Extension of the Role of the Auxiliary su(2)-Algebra ---

The role of the auxiliary su(2)-algebra proposed by the present authors in the latest paper is extended. Its aim is to determine the minimum weight states completely. With the aid of scalar operators for the auxiliary algebra, new aspects are added to the minimum weight states in the aligned scheme discussed in the latest paper. Some simple examples are shown.

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arXiv2011

Background of the su(2)-Algebraic Many-Fermion Models in the Boson Realization

The su(2)-algebraic many-fermion model is formulated so as to be able to get the unified understanding of the structures of three simple models: the single-level pairing, the isoscalar proton-neutron pairing and the two-level Lipkin model. Basic idea is to introduce an auxiliary su(2)-algebra, any generator of which commutes with any generator of the starting su(2)-algebra. With the aid of this algebra, the minimum weight states are completely determined in a simple forms. Further, concerning the two algebras, boson realization is presented. Through this formulation, the behavior of the total fermion in the Lipkin model is notably different of those in the other two models. As supplementary problem, the boson-fermion realization and the Lipkin model in the isovector pairing model are investigated.

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arXiv2011

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.

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arXiv2011

On the Color-Singlet States in Many-Quark Model with the su(4)-Algebraic Structure. III

A phase structure and phase transitions are investigated in the modified Bonn quark model. The force strength, which represents the particle-hole type interaction, is devised so as to depend on the quark number, namely quark number density. As a result, it is shown that the phase transition from the quark-triplet state as a nucleon to the quark-pair state as a color-superconducting state occurs as the density increases.

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arXiv2010

Two-Level Lipkin Model in Unconventional Boson Realization

With the aim of applying to the Lipkin model in the case of open shell system, a possible form of the boson realization for the su(2)-algebra is proposed both in the Schwinger and the Holstein-Primakoff representation. The basic idea is borrowed from the Schwinger boson realization for the su(4)-algebra for many-quark system recently presented by the present authors. As the simplest approximation, a certain approximate form is given and the result is a natural generalization of the RPA result in the case of closed shell system.

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arXiv2010

First Order Quark-Hadron Phase Transition in the NJL-Type Nuclear and Quark Model

The quark-hadron phase transition at finite baryon chemical potential is investigated in the extended Nambu-Jona-Lasinio model in which the scalar-vector eight-point interaction is included holding the chiral symmetry. By comparing a pressure of the symmetric nuclear matter with that of the quark matter, the realized phase at given baryon density is determined. As a result, the first order quark-hadron phase transition is derived where the deconfinement transition occurs after the chiral symmetry restoration in this model.

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arXiv2009

Note on Many-Quark Model with su(4) Algebraic Structure

In a many-quark model developed in our previous paper where two-body color pairing and particle-hole type interactions are active, the exact energy eigenstates are re-formed with physically clearer expressions than those derived in our previous paper. By using the re-formed energy eigenstates, two types of the eigenstates in which the pairing correlation and the quark triplet formation separately appear definitely, are unified and this model can be treated for both the strong color correlations and the quark triplet formations.

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arXiv2009

On the Exact Eigenstates and the Ground States Based on the Boson Realization for Many-Quark Model with su(4) Algebraic Structure

Based on the boson realization, the ground state and phase structure are investigated in a many-quark model with algebraic structure developed in our previous paper, in which the two-body pairing and particle-hole type interactions are active. The physical interpretation of the exact eigenstates obtained in the boson realization in our previous paper is given in a many-quark model with su(4) algebraic structure.

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arXiv2008

Many-Quark Model with su(4) Algebraic Structure

With the use of a certain type of the Schwinger boson representation of the su(4) algebra, the Bonn model for many-quark systems and an extension of the model, in which the energies of the various exact states are controled, namely, the energies are enhanced or de-enhanced, are investigated. Especially, the triplet formation and the pairing correlation in many-quark states are discussed. In the boson space, all the results are analytically expressed in the exact forms.

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arXiv2008

Impact of eight-quark interactions in chiral phase transitions I: Secondary magnetic catalysis

The influence of a constant magnetic field on the order parameter of the four-dimensional Nambu and Jona-Lasinio model extended by the 't Hooft six-quark term and eight-quark interactions is considered. It is shown that the multi-quark interactions cause the order parameter to increase sharply (secondary magnetic catalysis) with increasing strength of the field at the characteristic scale $H\sim 10^{14}Λ^2$ G/MeV^2.

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arXiv2007

Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions

Catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions is considered. We use the three flavour Nambu -- Jona-Lasinio type model with 't Hooft and eight-quark interaction terms. It is shown that the multi-quark interactions introduce new additional features to this phenomenon: (a) the local minimum of the effective potential catalyzed by the constant magnetic field is smoothed out with increasing strength of the field at the characteristic scale H~10^{19} G, (b) the multi-quark forces generate independently another local minimum associated with a larger dynamical fermion mass. This state may exist even for multi-quark interactions with a subcritical set of couplings, and is globally stable with respect to a further increase of the magnetic field.

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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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