Centrality dependence of the multiplicity and transverse momentum distributions at RHIC and LHC and the percolation of strings

The dependence of the multiplicity and the transverse momentum distribution on the number of collisions are studied for central and peripheral Au-Au collisions at SPS, RHIC and LHC energies in the framework of percolation of strings. A scaling law relating the multiplicity to the mean transverse momentum is obtained. Our results are in overall agreement with the SPS and RHIC data, obtaining a suppression on $p_T$ distribution even for $p_T$ larger than 1 GeV/c.Comment: Contribution to QM2002, espcrc1.st

On polynomial submersions of degree 44 and the real Jacobian conjecture in R2\R^2

The main result of this paper is the following version of the real Jacobian conjecture: "Let $F=(p,q):\R^2\to\R^2$ be a polynomial map with nowhere zero Jacobian determinant. If the degree of $p$ is less than or equal to $4$, then $F$ is injective". Assume that two polynomial maps from $\R^2$ to $\R$ are equivalent when they are the same up to affine changes of coordinates in the source and in the target. We completely classify the polynomial submersions of degree $4$ with at least one disconnected level set up to this equivalence, obtaining four classes. Then, analyzing the half-Reeb components of the foliation induced by a representative $p$ of each of these classes, we prove there is not a polynomial $q$ such that the Jacobian determinant of the map $(p,q)$ is nowhere zero. Recalling that the real Jacobian conjecture is true for maps $F=(p,q)$ when all the level sets of $p$ are connected, we conclude the proof of the main result

Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states

We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates $\gamma$ and $\gamma_0$ and a single parameter $\Delta_{\mathrm{dd}}$ describing the dipole-dipole shifts. We solve the dynamics exactly for $N=2$ atoms, numerically for up to 30 atoms, and obtain the large-$N$-limit by amean-field approach. We find that there is a critical difference $\gamma_0-\gamma$ that depends on $N$ beyond which superradiance is lost. We show that exact non-trivial dark states (i.e. states other than the ground state with vanishing spontaneous emission) only exist for $\gamma=\gamma_0$, and that those states (dark when $\gamma=\gamma_0$) are subradiant when $\gamma<\gamma_0$.Comment: 14 pages, 8 figure

Modeling the Void H I Column Density Spectrum

The equivalent width distribution function (EWDF) of \hone absorbers specific to the void environment has been recently derived (Manning 2002), revealing a large line density of clouds (dN/dz ~500 per unit z for Log (N_HI)> 12.4). I show that the void absorbers cannot be diffuse (or so-called filamentary) clouds, expanding with the Hubble flow, as suggested by N-body/hydro simulations. Absorbers are here modeled as the baryonic remnants of sub-galactic perturbations that have expanded away from their dark halos in response to reionization at z ~ 6.5. A 1-D Lagrangian hydro/gravity code is used to follow the dynamic evolution and ionization structure of the baryonic clouds for a range of halo circular velocities. The simulation products at z=0 can be combined according to various models of the halo velocity distribution function to form a column density spectrum that can be compared with the observed. I find that such clouds may explain the observed EWDF if the halo velocity distribution function is as steep as that advanced by Klypin (1999), and the halo mass distribution is closer to isothermal than to NFW.Comment: 21 pages, 15 figures. Paper in press; ApJ 591, n

Efficient Subsidization of Human Capital Accumulation with Overlapping Generations and Endogenous Growth

This paper studies second best policies for education, saving, and labour in an OLG model in which endogenous growth results from human capital accumulation. Government expenditures have to be financed by linear instruments so that growth equilibria are inefficient. The inefficiency is exacerbated if selfish individuals externalize the positive effect of education on descendents’ productivity. It is shown to be second best to subsidize education even relative to the first best if the elasticity of the human capital investment function is strictly increasing.OLG model; endogenous growth; endogenous labour, education, and saving; intergenerational externalities; optimal taxation

Exact Study of the Effect of Level Statistics in Ultrasmall Superconducting Grains

The reduced BCS model that is commonly used for ultrasmall superconducting grains has an exact solution worked out long ago by Richardson in the context of nuclear physics. We use it to check the quality of previous treatments of this model, and to investigate the effect of level statistics on pairing correlations. We find that the ground state energies are on average somewhat lower for systems with non-uniform than uniform level spacings, but both have an equally smooth crossover from the bulk to the few-electron regime. In the latter, statistical fluctuations in ground state energies strongly depend on the grain's electron number parity.Comment: 4 pages, 3 eps figs, RevTe