Entanglement and particle correlations of Fermi gases in harmonic traps

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.Comment: 15 pages, 22 fig

Static and dynamic structure factors in three-dimensional randomly diluted Ising models

We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.Comment: 43 page

Expression of SPANX proteins in normal prostatic tissue and in prostate cancer

The sperm protein associated with the nucleus in the X chromosome (SPANX) gene family encodes for proteins that are not only expressed in germ cells, but also in a number of tumors. In addition, SPANX genes map in an interval of the X chromosome (namely, Xq27), which has been found to be associated with familial prostate cancer by linkage analysis. The aim of this study was therefore to evaluate SPANX protein expression in normal prostate tissues and in prostate carcinoma. For this purpose, formalin-fixed and paraffin-embedded sections obtained from 15 normal (at autopsy) donors and 12 men with prostate cancer were analyzed by immunohistochemistry. About 40% of both normal and tumor prostate samples resulted SPANX positive. Signals were exclusively within the nucleus in normal prostate cells, whereas both nuclear and cytoplasmic positivity was observed in tumor cells. In conclusion, these findings showed that SPANX genes are expressed in both normal and tumor prostate gland, but the latter showed a peculiar cytoplasmic staining positivity. This suggests a possible association between SPANX over expression and prostate cancer development. Additional studies are needed to corroborate this hypothesis

Strong coupling expansion of chiral models

A general precedure is outlined for an algorithmic implementation of the strong coupling expansion of lattice chiral models on arbitrary lattices. A symbolic character expansion in terms of connected values of group integrals on skeleton diagrams may be obtained by a fully computerized approach.Comment: 2 pages, PostScript file, contribution to conference LATTICE '9

Large-N phase transition in lattice 2-d principal chiral models

We investigate the large-N critical behavior of 2-d lattice chiral models by Monte Carlo simulations of U(N) and SU(N) groups at large N. Numerical results confirm strong coupling analyses, i.e. the existence of a large-N second order phase transition at a finite $\beta_c$.Comment: 12 pages, Revtex, 8 uuencoded postscript figure

Critical behavior of the random-anisotropy model in the strong-anisotropy limit

We investigate the nature of the critical behavior of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition metals. In particular, we consider the strong-anisotropy limit (SRAM), in which the Hamiltonian can be rewritten as the one of an Ising spin-glass model with correlated bond disorder. We perform Monte Carlo simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring correlation functions of the replica-replica overlap, which is the order parameter at a glass transition. The corresponding results show critical behavior and finite-size scaling. They provide evidence of a finite-temperature continuous transition with critical exponents $\eta_o=-0.24(4)$ and $\nu_o=2.4(6)$. These results are close to the corresponding estimates that have been obtained in the usual Ising spin-glass model with uncorrelated bond disorder, suggesting that the two models belong to the same universality class. We also determine the leading correction-to-scaling exponent finding $\omega = 1.0(4)$.Comment: 24 pages, 13 figs, J. Stat. Mech. in pres

Universality class of 3D site-diluted and bond-diluted Ising systems

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, $\nu=0.683(2)$, $\eta=0.036(1)$, $\alpha=-0.049(6)$, $\gamma=1.341(4)$, $\beta=0.354(1)$, $\delta=4.792(6)$, and of the leading and next-to-leading correction-to-scaling exponents, $\omega=0.33(3)$ and $\omega_2=0.82(8)$.Comment: 45 pages, 22 figs, revised estimate of n

Merging of globular clusters within inner galactic regions. I. Do they survive the tidal interaction?

The main topic of this paper is the investigation of the modes of interaction of globular clusters (GCs) moving in the inner part of a galaxy. This is tackled by means of high-resolution N-body simulations, whose first results are presented in this article. Our simulations dealt with primordial very massive (order of 10^7 solar masses) GCs that were able to decay, because of dynamical friction, into the inner regions of triaxial galaxies on a time much shorter than their internal relaxation time. To check the disruptive role of both tidal forces and GC-GC collisions, we maximised the tidal interaction considering GCs on quasi-radial orbits. The available CPU resources allowed us to follow 8 oscillations of the GCs along their orbits and the main findings are: i) clusters with an initial high enough King concentration parameter (c>=1.2), preserve up to 50% of their initial mass; ii) the inner density distribution of the survived clusters keep a King model profile; iii) GC-GC collisions have a negligible effect with respect to that caused by the passage through the galactic center; iv) the orbital energy dissipation due to the tidal interaction is of the same order of that caused by dynamical friction; v) complex sub-structures like "ripples" and "clumps" formed, as observed around real clusters. These findings support the validity of the hypothesis of merging of GCs in the galactic central region, with modes that deserve further careful investigations.Comment: LaTeX 2e, AASTeX v5.x, 23 pages with 14 figures. Accepted for publication on the Astrophysical Journal. Final version with major change

Resummation of Cactus Diagrams in Lattice QCD

We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corresponding nonperturbative estimates.Comment: 18 page