arXiv subjects

C. Providencia

Publications and source records attributed to C. Providencia.

At least 73 records · Page 4Linked to original sources

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

arXiv2006

Collective modes in relativistic npe matter at finite temperature

Isospin and density waves in neutral neutron-proton-electron (npe) matter are studied within a relativistic mean-field hadron model at finite temperature with the inclusion of the electromagnetic field. The dispersion relation is calculated and the collective modes are obtained. The unstable modes are discussed and the spinodals, which separate the stable from the unstable regions, are shown for different values of the momentum transfer at various temperatures. The critical temperatures are compared with the ones obtained in a system without electrons. The largest critical temperature, 12.39 MeV, occurs for a proton fraction y_p=0.47. For y_p=0.3 we get $T_{cr}$ =5 MeV and for y_p>0.495 $T_cr\lesssim 8$ MeV. It is shown that at finite temperature the distillation effect in asymmetric matter is not so efficient and that electron effects are particularly important for small momentum transfers.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

arXiv2005

Quark stars within relativistic models

Lately, it has been suggested that strange (quark) stars can be responsible for glitches and other observational features of pulsars. Some discussions on whether quark stars, if really exist, are bare or crusted are also a source of controversy in the recent literature. In the present work we use the Nambu-Jona-Lasinio model, known to incorporate chiral symmetry, necessarily present in the QCD formalism, in order to describe quark star properties. We compare our results for the stars and the features of the model with the much simpler model normally used in the description of strange stars, namely the MIT bag model. We also investigate the differences in the stellar properties which arise due to the presence of the crust. We show that the NJL model produces results which are somewhat different as compared with the MIT model.

astro-ph↗

arXiv2005

Kaon condensation in the quark-meson coupling model and compact stars

The properties of neutron stars constituted of a crust of hadrons and an internal part of hadrons and kaon condensate are calculated within the quark-meson-coupling model. We have considered stars with nucleons only in the hadron phase and also stars with hyperons as well. The results are compared with the ones obtained from the non-linear Walecka model for the hadronic phase.

astro-ph↗

arXiv2005

Relativistic Equation of state with short range correlations

Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The effect of the correlations in the ground state properties of the nuclear matter is studied.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗