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The quartic term in the framework of relativistic mean field theory with inclusion of scalar meson interactions is investigated. It is shown that the quartic term in the asymmetric expansion of nuclear matter energy may reach very large values. This makes the even power expansion of asymmetry questionable and suggests possible non-analytic contributions to the energy of matter., Comment: 5 pages, 3 figures, accepted to Phys.Rev. C

Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics relative to such braid classes and define a braid Floer homology. This refinement of the Floer homology originally used for the Arnol'd Conjecture yields a Morse-type forcing theory for periodic points of area-preserving diffeomorphisms of the 2-disc based on braiding. Contributions of this paper include (1) a monotonicity lemma for the behavior of the nonlinear Cauchy-Riemann equations with respect to algebraic lengths of braids; (2) establishment of the topological invariance of the resulting braid Floer homology; (3) a shift theorem describing the effect of twisting braids in terms of shifting the braid Floer homology; (4) computation of examples; and (5) a forcing theorem for the dynamics of Hamiltonian disc maps based on braid Floer homology., Comment: This is a "verbose" version of an article submitted to a special issue on "Future Directions in Dynamical Systems"

We present a quantum critical behavior of the renormalized single-particle Wannier function, calculated in the Gutzwiller correlated state near the insulator-metal transition (IMT) for cubic lattices. The wave function size and its maximum, as well as the system energy scale with increasing lattice parameter $R$ as $R^{n}$. Such scaling is interpreted as the evidence of a dominant role of the Coulomb repulsion. Relation of the insulator-metal transition lattice-parameter value $R=R_{C}$ to the original {\em Mott criterion\} is obtained. The method is tested by comparing our results with the exact approach for the Hubbard chain., Comment: 6 pages, 6 figures, 1 table

We study the localization of protons in the core of neutron stars for ten realistic nuclear models that share a common behaviour of nuclear symmetry energy which saturates and eventually decreases at high densities. This results in the low proton fraction of beta-stable neutron star matter. Protons form a small admixture in the neutron star core, which is localized at sufficiently high densities. For every model we calculate the density $n_{loc}$ above which the localization effect is present. Our results indicate that localization occurs at densities above $0.5-1.0 fm^{-3}$. The phase with localized protons occupies a spherical shell or a core region inside neutron stars which contains significant fraction of all nucleons. Proton localization is of great importance for astrophysical properties of neutron stars as it strongly affects transport coefficients of neutron star matter and can produce spontaneous magnetization in neutron stars., Comment: 6 pages, 3 figures, Presented at the XXIX Mazurian Lakes Conference on Physics, Piaski, Poland, August 30 - Septenber 6, 2005

Recently observed splitting in angular resolved photoemission spectroscopy (ARPES) on $\chem{Bi_2Sr_{2-x}La_xCuO_{6+\delta}}$ high--temperature superconductor (Janowitz C. {\it et al.}, {\it Europhys. Lett.}, {\bf 60} (2002) 615) is interpreted within the phenomenological Luttinger--liquid framework, in which both the non--Fermi liquid scaling exponent of the spectral function and the spin--charge separation are introduced. The anomalous Green function with adjustable parameters fits very well to the Fermi edge and the low--energy part of ARPES along the $\Gamma-M$ line in the Brillouin zone. In contrast to one--dimensional models with Luttinger--liquid behavior we find that both the anomalous scaling $\alpha$ and the parameter $\delta$ describing the spin--charge separation are momentum dependent. The higher--energy part of the spectra is not accounted for by this simple Luttinger--liquid form of the Green function. In this energy regime additional scattering processes are plausible to produce the experimentally observed wide incoherent background, which diminishes as the inverse of the energy., Comment: 7 pages, 3 figures, EPL style

We summarize briefly the main results obtained within the proposed EDABI method combining Exact Diagonalization of (parametrized) many-particle Hamiltonian with Ab Initio self-adjustment of the single-particle wave function in the correlated state of interacting electrons. The properties of nanoscopic chains and rings are discussed as a function of their interatomic distance R and compared with those obtained by Bethe ansatz for infinite Hubbard chain. The concepts of renormalized orbitals, distribution function in momentum space, and of Hubbard splitting as applied to nanoscopic systems are emphasized., Comment: 22 pages, 12 figures. Submitted to Proceedings of the NATO Advanced Research Workshop: Molecular Nanowires and other Quantum Objects, Kluwer Publ., Dordrecht, 2004

We supplement (and critically overview) the existing extensive analysis of antiferromagnetic solution for the Hubbard model with a detailed discussion of two specific features, namely (i) the evolution of the magnetic (Slater) gap (here renormalized by the electronic correlations) into the Mott-Hubbard or atomic gap, and (ii) a rather weak renormalization of the effective mass by the correlations in the half-filled-band case, which contrasts with that for the paramagnetic case. The mass remains strongly enhanced in the non-half-filled-band case. We also stress the difference between magnetic and non-magnetic contributions to the gap. These results are discussed within the slave boson approach in the saddle-point approximation, in which there appears a non-linear staggered molecular field due to the electronic correlations that leads to the appearance of the magnetic gap. They reproduce correctly the ground-state energy in the limit of strong correlations. A brief comparison with the solution in the limit of infinite dimensions and the corresponding situation in the doubly-degenerate-band case with one electron per atom is also made., Comment: 17 pages with 9 figures, the revised and published version

We study properties of the proton component of neutron star matter for a number of realistic nuclear models. Protons which form a few percent admixture tend to be localized in potential wells corresponding to neutron matter inhomogeneities created by the protons in the neutron medium. We calculate the energy of the Wigner-Seitz cell enclosing a single localized proton. The neutron background is treated in the Thomas-Fermi approximation and the localized proton is described by the Gaussian wave function. The neutron density profile is obtained by solving the appropriate variational equation. This approach gives lower energies of localized protons than obtained previously with less sophisticated methods., Comment: LaTeX with the APPolB style (included), 10 pages, 16 figures, to appear in Acta Physica Polonica B