Approximation by the Dickman distribution and quasi-logarithmic combinatorial structures

Quasi-logarithmic combinatorial structures are a class of decomposable combinatorial structures which extend the logarithmic class considered by Arratia, Barbour and Tavar\'{e} (2003). In order to obtain asymptotic approximations to their component spectrum, it is necessary first to establish an approximation to the sum of an associated sequence of independent random variables in terms of the Dickman distribution. This in turn requires an argument that refines the Mineka coupling by incorporating a blocking construction, leading to exponentially sharper coupling rates for the sums in question. Applications include distributional limit theorems for the size of the largest component and for the vector of counts of the small components in a quasi-logarithmic combinatorial structure.Comment: 22 pages; replaces earlier paper [arXiv:math/0609129] with same title by Bruno Nietlispac

Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)

The critical and asymptotic behaviors of solutions of the sixth Painlev\'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.Comment: 30 pages, 1 figure; Nonlinearity 201

Superconducting states of pure and doped graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states, s-wave and an exotic $p+ip$ that is possible because of the special structure of the honeycomb lattice. At half filling, the $p+ip$ phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.Comment: 4 pages, 6 figure

On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

We study the solutions of the sixth Painlev\'e equation with a logarithmic asymptotic behavior at a critical point. We compute the monodromy group associated to the solutions by the method of monodromy preserving deformations and we characterize the asymptotic behavior in terms of the monodromy itself.Comment: LaTeX with 8 figure

Strong D* -> D+pi and B* -> B+pi couplings

We compute g_{D* D pi} and g_{B* B pi} using a framework in which all elements are constrained by Dyson-Schwinger equation studies of QCD, and therefore incorporates a consistent, direct and simultaneous description of light- and heavy-quarks and the states they may constitute. We link these couplings with the heavy-light-meson leptonic decay constants, and thereby obtain g_{D* D pi}=15.9+2.1/-1.0 and g_{B* B pi}=30.0+3.2/-1.4. From the latter we infer \hat-g_B=0.37+0.04/-0.02. A comparison between g_{D* D pi} and g_{B* B pi} indicates that when the c-quark is a system's heaviest constituent, Lambda_{QCD}/m_c-corrections are not under good control.Comment: 5 pages, 1 table, 2 figure

Coulomb force effects in low-energy α\alpha-deuteron scattering

The $\alpha$-proton Coulomb interaction is included in the description of $\alpha$-deuteron scattering using the screening and renormalization approach in the framework of momentum-space three-particle equations. The technical reliability of the method is demonstrated. Large Coulomb-force effects are found.Comment: To be published in Phys. Rev.

1/N Expansion in Correlated Graphene

We examine the 1/N expansion, where N is the number of two-component Dirac fermions, for Coulomb interactions in graphene with a gap of magnitude $\Delta = 2 m$. We find that for $N\alpha\gg1$, where $\alpha$ is graphene's "fine structure constant", there is a crossover as a function of distance $r$ from the usual 3D Coulomb law, $V(r) \sim 1/r$, to a 2D Coulomb interaction, $V(r) \sim \ln(N\alpha/mr)$, for $m^{-1} \ll r \ll m^{-1} N \alpha/6$. This effect reflects the weak "confinement" of the electric field in the graphene plane. The crossover also leads to unusual renormalization of the quasiparticle velocity and gap at low momenta. We also discuss the differences between the interaction potential in gapped graphene and usual QED for different coupling regimes.Comment: 7 pages, 2 figures; expanded presentation, references adde

Quantum size effects in the low temperature layer-by-layer growth of Pb on Ge(001)

The electronic properties of thin metallic films deviate from the corresponding bulk ones when the film thickness is comparable with the wavelength of the electrons at the Fermi level due to quantum size effects (QSE). QSE are expected to affect the film morphology and structure leading to the low temperature (LT) ``electronic growth'' of metals on semiconductors. In particular, layer-by-layer growth of Pb(111) films has been reported for deposition on Ge(001) below 130 K. An extremely flat morphology is preserved throughout deposition from four up to a dozen of monolayers. These flat films are shown to be metastable and to reorganize into large clusters uncovering the first Pb layer, pseudomorphic to the substrate, already at room temperature. Indications of QSE induced structural variations of the growing films have been reported for Pb growth on Ge(001), where the apparent height of the Pb(111) monatomic step was shown to change in an oscillatory fashion by He atom scattering (HAS) during layer-by-layer growth. The extent of the structural QSE has been obtained by a comparison of the HAS data with X-ray diffraction (XRD) and reflectivity experiments. Whereas step height variations as large as 20 % have been measured by HAS reflectivity, the displacement of the atomic planes from their bulk position, as measured by XRD, has been found to mainly affect the topmost Pb layer, but with a lower extent, i.e. the QSE observed by HAS are mainly due to a perpendicular displacement of the topmost layer charge density. The effect of the variable surface relaxation on the surface vibration has been studied by inelastic HAS to measure the acoustic dispersion of the low energy phonons.Comment: 28 pages (laTex,elsart) and 13 figures (eps); updated reference