Mean-field expansion and meson effects in chiral condensate of analytically regularized Nambu -- Jona-Lasinio model

Scalar meson contributions in chiral quark condensate are calculated for analytically regularized Nambu -- Jona-Lasinio model in framework of mean-field expansion in bilocal-source formalism. Sigma-meson contribution for physical values of parameters is found to be small. Pion contribution is found to be significant and should be taken into account at the choice of the parameter values.Comment: 12 pages, Plain LaTex, no figures, final versio

Efficiency of Government Social Spending in Croatia

This paper analyzes the relative efficiency of social spending and service delivery in Croatia by comparing social spending and key social (outcome) indicators in Croatia to those of comparator countries. The analysis finds evidence of significant inefficiencies in Croatia’s social spending, mainly related to inadequate cost recovery for health and education services, weaknesses in the financing mechanisms and institutional arrangements, weak competition in the provision of social services, and weaknesses in targeting benefits. The paper also identifies areas for cost recovery and reform.Expenditure efficiency; health care spending; education spending; social protection spending

Transition to sub-Planck structures through the superposition of q-oscillator stationary states

We investigate the superposition of four different quantum states based on the q-oscillator. These quantum states are expressed by means of Rogers-Szego polynomials. We show that such a superposition has the properties of the quantum harmonic oscillator when q -> 1, and those of a compass state with the appearance of chessboard-type interference patterns when q -> 0

A superintegrable finite oscillator in two dimensions with SU(2) symmetry

A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is found that the dynamical difference eigenvalue equation can be written in terms of creation and annihilation operators. The wavefunctions of the Hamiltonian are expressed in terms of two known families of bivariate Krawtchouk polynomials; those of Rahman and those of Tratnik. These polynomials form bases for SU(2) irreducible representations. It is further shown that the pair of eigenvalue equations for each of these families are related to each other by an SU(2) automorphism. A finite model of the anisotropic oscillator that has wavefunctions expressed in terms of the same Rahman polynomials is also introduced. In the continuum limit, when the number of grid points goes to infinity, standard two-dimensional harmonic oscillators are obtained. The analysis provides the $N\rightarrow \infty$ limit of the bivariate Krawtchouk polynomials as a product of one-variable Hermite polynomials

Quantum oscillator models with a discrete position spectrum in the framework of Lie superalgebras

We present some algebraic models for the quantum oscillator based upon Lie superalgebras. The Hamiltonian, position and momentum operator are identified as elements of the Lie superalgebra, and then the emphasis is on the spectral analysis of these elements in Lie superalgebra representations. The first example is the Heisenberg-Weyl superalgebra sh(2 vertical bar 2), which is considered as a "toy model". The representation considered is the Fock representation. The position operator has a discrete spectrum in this Fock representation, and the corresponding wavefunctions are in terms of Charlier polynomials. The second example is sl(2 vertical bar 1), where we construct a class of discrete series representations explicitly. The spectral analysis of the position operator in these representations is an interesting problem, and gives rise to discrete position wavefunctions given in terms of Meixner polynomials. This model is more fundamental, since it contains the paraboson oscillator and the canonical oscillator as special cases