arXiv subjects
Publications and source records attributed to C. Providencia.
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.
The periods of the harmonic oscillations of the ion core of charged sodium clusters around the equilibrium shapes are considered. It is found that these periods are of the order of magnitude of the experimentally measured relaxation times of the plasmons, which suggests the importance of the electron-ion coupling and stresses the role played by the electron-phonon interaction in the dissipation of the plasmon energy. The relation of the process to fission is briefly discussed.
The existence of phase transitions from liquid to gas phases in asymmetric nuclear matter (ANM) is related with the instability regions which are limited by the spinodals. In this work we investigate the instabilities in ANM described within relativistic mean field hadron models, both with constant and density dependent couplings at zero and finite temperatures. In calculating the proton and neutron chemical potentials we have used an expansion in terms of Bessel functions that is convenient at low densities. The role of the isovector scalar $δ$-meson is also investigated in the framework of relativistic mean field models and density dependent hadronic models. It is shown that the main differences occur at finite temperature and large isospin asymmetry close to the boundary of the instability regions.
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.
The properties of hybrid stars formed by hadronic and quark matter in beta-equilibrium at fixed entropies are described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. In this work we include the possibility of neutrino trapped EOS and compare the star properties with the ones obtained after deleptonization, when neutrinos have already diffused out. We use the nonlinear Walecka model for the hadron matter with two different sets for the hyperon couplings and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The phase transition to a deconfined quark phase is investigated. Depending on the model and the parameter set used, the mixed phase may or may not exist in the EOS at high densities. The star properties are calculated for each equation of state. The maximum mass stellar configurations obtained within the NJL have larger masses than the ones obtained within the Bag model. The Bag model predicts a mixed phase in the interior of the most massive stable stars while, depending on the hyperon couplings, the NJL model predicts a mixed phase or pure quark matter. Comparing with neutrino free stars, the maximum allowed baryonic masses for protoneutron stars are $\sim 0.4 M_\odot$ larger for the Bag model and $\sim 0.1 M_\odot$ larger for the NJL model when neutrino trapping is imposed.
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.
We investigate the properties of mixed stars formed by hadronic and quark matter in $β$-equilibrium described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. We use the non- linear Walecka model for the hadron matter and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The phase transition to a deconfined quark phase is investigated. In particular, we study the dependence of the onset of a mixed phase and a pure quark phase on the hyperon couplings, quark model and properties of the hadronic model. We calculate the strangeness fraction with baryonic density for the different EOS. With the NJL model the strangeness content in the mixed phase decreases. The calculations were performed for T=0 and for finite temperatures in order to describe neutron and proto-neutron stars. The star properties are discussed. Both the Bag model and the NJL model predict a mixed phase in the interior of the star. Maximum allowed masses for proto-neutron stars are larger for the NJL model ($\sim 1.9$ M$_{\bigodot}$) than for the Bag model ($\sim 1.6$ M$_{\bigodot}$).
A simple derivation of an explicitly rotational invariant Lagrangian describing the dynamics of an antiferromagnetic spin system is presented. The scope of the derived Lagrangian is analysed in the context of schematic models. It is shown that the Lagrangian describes the behaviour of spin systems from the anti-ferromagnetic to the ferromagnetic regimes.
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.
With the aim of constructing coherent states for many-body systems consisting of six kinds of boson operators, a possible form of the orthogonal set is presented in terms of monomial with respect to state generating operators. In connection with the su(3)-, the su(2)-, the su(2,1)- and the su(1,1)-algebras, four types of the orthogonal set are discussed.
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.
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.
A possible scheme of q-deformation, which was recently developed by the present authors, is reviewed by stressing the starting idea.
Following the deformed boson scheme leading to the su(1,1)-algebra, a certain simple boson system is deformed in the framework of the second Holstein-Primakoff representation. With the aid of the MYT boson mapping, the second representation arrives at the first Holstein-Primakoff representation. The su(1,1)-algebraic model obtained in this procedure is compared with that in the Schwinger representation investigated by three of the present authors (A.K., Y.T. and M.Y.).
The deformed boson scheme in four kinds of boson operators, which was recently proposed by the present authors, is supplemented by the T-type deformation closely related with the su(1,1)-algebra. Two subjects are discussed in relation to the S-type deformation closely related with the su(2)-algebra.
Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent state given by the present authors is generalized and the su(2)_q- and the su(1,1)_q-algebras are obtained in the form expressed in terms of four kinds of boson operators. As an illustrative example of the application, the framework for describing thermal effects observed in two-level shell model under the pairing correlation is proposed.
The treatment for the multiboson coherent state is extended for the completeness of the formulation. The basic idea for the extension is presented in terms of expanding the boson space. The MYT boson mapping plays a central role. The resultant multiboson coherent state includes the state obtained in our previous treatment and the form suggests various multiboson coherent states are possible in the deformed boson scheme.
Two types of boson-pair coherent states, which were proposed independently by the present authors, are investigated. Main conclusion is as follows : Although the two states are superposed contrastively in terms of the boson-pairs, the expectation values of the boson-pair operators for these states are the same as one another with high accuracy.