An inverse indefinite numerical range problem

https://thekeep.eiu.edu/den_1997_feb/1008/thumbnail.jp

A new description of motion of the Fermionic SO(2N+2) top in the classical limit under the quasi-anticommutation relation approximation

The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidian space (N: number of single-particle states of the fermions). The images of fermion annihilation-creation operators must satisfy the canonical anti-commutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree-Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle-hole plus BCS type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation, due to the unpaired-mode effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi anti-commutation-relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters k and l in the Lagrange multipliers can be determined withuout any inconcistency.Comment: 36 pages, no figures, typos corrected, published versio

Aspects of short range correlations in a relativistic model

In the present work short range correlations are introduced for the first time in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation using an effective Hamiltonian derived from the $\sigma-\omega$ Walecka model. The unitary correlation method is used to introduce short range correlations. The effect of the correlations in the ground state properties of the nuclear matter is discussed.Comment: 7 pages, 3 figure

Color symmetrical superconductivity in a schematic nuclear quark model

In this note, a novel BCS-type formalism is constructed in the framework of a schematic QCD inspired quark model, having in mind the description of color symmetrical superconducting states. The physical properties of the BCS vacuum (average numbers of quarks of different colors) remain unchanged under an arbitrary color rotation. In the usual approach to color superconductivity, the pairing correlations affect only the quasi-particle states of two colors, the single particle states of the third color remaining unaffected by the pairing correlations. In the theory of color symmetrical superconductivity here proposed, the pairing correlations affect symmetrically the quasi-particle states of the three colors and vanishing net color-charge is automatically insured. It is found that the groundstate energy of the color symmetrical sector of the Bonn model is well approximated by the average energy of the color symmetrical superconducting state proposed here

Electron--phonon coupling and anharmonic effects in metal clusters

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.Comment: 6 pages, no figures, to appear in EPLetter

Short range correlations in relativistic nuclear matter models

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. It is shown that the correlations give rise to an extra node in the ground-state wave-function in the nucleons, contrary to what happens in non-relativistic calculations with a hard core. The effect of the correlations in the ground state properties of the nuclear matter and neutron matter is studied. The nucleon effective mass and equation of state (EOS) are very sensitive to short range correlations. In particular, if the pion contact term is neglected a softening of the EOS is predicted. Correlations have also an important effect on the neutron matter EOS which presents no binding but only a very shallow minimum contrary to the Walecka model.Comment: 8pages, 4 figure

A Relativistic Thomas-Fermi Description of Collective Modes in Droplets of Nuclear Matter

Isoscalar collective modes in a relativistic meson-nucleon system are investigated in the framework of the time-dependent Thomas-Fermi method. The energies of the collective modes are determined by solving consistently the dispersion relations and the boundary conditions. The energy weighted sum rule satisfied by the model allows the identification of the giant ressonances. The percentage of the energy weighted sum rule exhausted by the collective modes is in agreement with experimental data, but the energies come too high.Comment: 21 pages (RevTex) and 2 postscript figures as a compressed uuencode fil

Stellar matter with a strong magnetic field within density-dependent relativistic models

The effect of strong magnetic fields on the equation of state (EoS) for compact stars described with density-dependent relativistic hadronic models is studied. A comparison with other mean-field relativistic models is done. It is shown that the largest differences between models occur for low densities, and that the magnetic field affects the crust properties of a star, namely its extension.Comment: 21 pages, 10 figures and 2 table

Warm stellar matter with deconfinement: application to compact stars

We investigate the properties of mixed stars formed by hadronic and quark matter in $\beta$-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$_{\bigodot}$).Comment: RevTeX,14 figures, accepted to publication in Physical Review