João da Providência

Corrections to the gaussian overlap approximation: A new boson expansion

Abstract The Gaussian overlap approximation is applied to Lipkins solvable model, both for a weak and for a strong interaction, in order to obtain insight on the conditions for the validity of that approximation. By carrying the expansions in the generator coordinate to higher orders, corrections to the harmonic approximation are obtained and applied, also with good results, to Lipkins model.

Some remarks on a conjecture of de Oliveira

Abstract Let U n be the group of the unitary n × n matrices. Let A =diag(α 1 ,…,α n ), B =diag(β 1 ,…,β n ), where α 1 ,…,α n , β 1 ,…,β n are complex numbers. A class of normal matrices satisfying the inclusion { det (A+UBU ∗ ):U∈μ n } ⊆ Co { ∏n i=1 (α i +β σ(i) :σ∈ S n } , where Co{} is the convex hull of {} and S n is the symmetric group of degree n , is obtained.

Effective Potential Approach to Quark Ferromagnetization in High Density Quark Matter

A possibility of spontaneous magnetization in high density symmetric quark matter is investigated using the NJL type effective model of QCD by means of an effective potential with respect to an auxiliary field. It is shown that the quark ferromagnetic condensate has non-vanishing value at high baryon density due to the tensor-type four-point interaction between quarks. Subject Index: 230

The Validity of the Marcus - de Oliveira Conjecture for Essentially Hermitian Matrices

Abstract Let X,Y be matrices of spectra x 1 ,…, x n and y 1 ,…, y n , respectively. For a wide class of pairs of essentially Hermitian matrices X,Y , we prove that the determinant of X+Y belongs to the convex hull of the n ! points п n i1 (x i +y σi ) (σ∈S n ).

On a conjecture of G. N. de Oliveira on determinants

Let A and B be complex diagonal n × A matrices with A = diag (a 1, …an )B = diag (b 1, …bn ). De Oliveiras conjecture where Co means the convex hull and S n is the symmetric group of degree n, is shown to be true in the case n = 3.

SPIN POLARIZATION IN HIGH DENSITY QUARK MATTER

We investigate the occurrence of a ferromagnetic phase transition in high density hadronic matter (e.g., in the interior of a neutron star). This could be induced by a four-fermion interaction analogous to the one which is responsible for chiral symmetry breaking in the Nambu–Jona-Lasinio model, to which it is related through a Fierz transformation. Flavor SU(2) and flavor SU(3) quark matter are considered. A second-order phase transition is predicted at densities about 5 times the normal nuclear matter density. It is also found that in flavor SU(3) quark matter, a first-order transition from the so-called 2 flavor super-conducting phase to the ferromagnetic phase arises. The color-flavor-locked phase may be completely hidden by the FP.

The q-deformed Moszkowski model: RPA modes

The behaviour of the Moszkowski model within the context of quantum algebras is studied. The Moszkowski Hamiltonian is exactly diagonalized for various values of the deformation parameter of the involved quantum algebra. The phase transition from a vibrational regime to a rotational regime is discussed in terms of the q-deformation. A coherent state for the ground state is introduced, and the Hartree-Fock energy and the RPA frequencies are compared with the exact values. The meaning of the q-deformation in this model is discussed.

Some results on the numerical range of a derivation

Let

The Hartree-Fock and Generator Coordinate Methods in field theory. The polaron problem

A \in \mathbb{C}_{n \times n}

Spin polarization versus color–flavor locking in high-density quark matter

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