Polarization anisotropy in the optical properties of silicon ellipsoids

A new real space quantum mechanical approach with local field effects included is applied to the calculation of the optical properties of silicon nanocrystals. Silicon ellipsoids are studied and the role of surface polarization is discussed in details. In particular, surface polarization is shown to be responsible for a strong optical anisotropy in silicon ellipsoids, much more pronounced with respect to the case in which only quantum confinement effects are considered. The static dielectric constant and the absorption spectra are calculated, showing that the perpendicular and parallel components have a very different dependence on the ellipsoid aspect ratio. Then, a comparison with the classical dielectric model is performed, showing that the model only works for large and regular structures, but it fails for thin elongated ellipsoids.Comment: 5 pages, 4 figures, International Conference on NANO-Structures Self-Assemblin

Trade in secured debt, adjustment in haircuts and international portfolios

I study the composition of international portfolios under collateral constraints and the implied cross-border transmission of shocks. I develop an international portfolio model with these features, in which leveraged investors seek diversification in both assets and secured liabilities and in which the pledgeable portion of assets adjusts to the state of the economy, reflecting borrowers’ credit risk. The new analytical results are as follows. First, agents choose endogenously how much to borrow from each country. Second, the collateral constraint, being a contractual link between secured and unsecured financial instruments, permits to compute portfolios without an arbitrage condition between those classes of assets. Finally, haircuts adjust endogenously through the change in the collateral values. After estimating the parameters governing this adjustment, I find that both portfolios and international transmission mechanism are quite sensitive to leveraged investors’ funding. As for portfolios, secured bonds have particularly effective hedging properties in managing the terms of trade risk. As for the international transmission, tightening haircuts affect the economic slowdown: initially severe contractions are followed by quick reversions to the long-term equilibrium. On a cumulative basis, these two effects compensate if haircuts adjust precisely to the economic state. But in case of uncertainty about this adjustment, collateral constraints are a source of risk which cannot be internationally diversified.Financial flows, borrowing limits, creditworthiness, risk premia, international business cycle, macroeconomic interdipendence.

Tight binding formulation of the dielectric response in semiconductor nanocrystals

We report on a theoretical derivation of the electronic dielectric response of semiconductor nanocrystals using a tight-binding framework. Extending to the nanoscale the Hanke and Sham approach [Phys. Rev. B 12, 4501 (1975)] developed for bulk semiconductors, we show how local field effects can be included in the study of confined systems. A great advantage of this scheme is that of being formulated in terms of localized orbitals and thus it requires very few computational resources and times. Applications to the optical and screening properties of semiconductor nanocrystals are presented here and discussed. Results concerning the absorption cross section, the static polarizability and the screening function of InAs (direct gap) and Si (indirect gap) nanocrystals compare well to both first principles results and experimental data. We also show that the present scheme allows us to easily go beyond the continuum dielectric model, based on the Clausius-Mossotti equation, which is frequently used to include the nanocrystal surface polarization. Our calculations indicate that the continuum dielectric model, used in conjunction with a size dependent dielectric constant, underestimates the nanocrystal polarizability, leading to exceedingly strong surface polarization fields.Comment: 9 pages, 5 figures; corrected typos, added reference

Sharp estimates for the first pp-Laplacian eigenvalue and for the pp-torsional rigidity on convex sets with holes

We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.Comment: 17 page

The impact of metallicity and dynamics on the evolution of young star clusters

The early evolution of a dense young star cluster (YSC) depends on the intricate connection between stellar evolution and dynamical processes. Thus, N-body simulations of YSCs must account for both aspects. We discuss N-body simulations of YSCs with three different metallicities (Z=0.01, 0.1 and 1 Zsun), including metallicity-dependent stellar evolution recipes and metallicity-dependent prescriptions for stellar winds and remnant formation. We show that mass-loss by stellar winds influences the reversal of core collapse. In particular, the post-collapse expansion of the core is faster in metal-rich YSCs than in metal-poor YSCs, because the former lose more mass (through stellar winds) than the latter. As a consequence, the half-mass radius expands more in metal-poor YSCs. We also discuss how these findings depend on the total mass and on the virial radius of the YSC. These results give us a clue to understand the early evolution of YSCs with different metallicity.Comment: to appear in "Massive Young Star Clusters Near and Far: From the Milky Way to Reionization", 2013 Guillermo Haro Conference, Eds. Y. D. Mayya, D. Rosa-Gonzalez & E. Terlevich, INAOE and AMC. 4 pages, 2 figure

Forming circumnuclear disks and rings in galactic nuclei: a competition between supermassive black hole and nuclear star cluster

We investigate the formation of circumnuclear gas structures from the tidal disruption of molecular clouds in galactic nuclei, by means of smoothed particle hydrodynamics simulations. We model galactic nuclei as composed of a supermassive black hole (SMBH) and a nuclear star cluster (NSC) and consider different mass ratios between the two components. We find that the relative masses of the SMBH and the NSC have a deep impact on the morphology of the circumnuclear gas. Extended disks form only inside the sphere of influence of the SMBH. In contrast, compact rings naturally form outside the SMBH's sphere of influence, where the gravity is dominated by the NSC. This result is in agreement with the properties of the Milky Way's circumnuclear ring, which orbits outside the SMBH sphere of influence. Our results indicate that compact circumnuclear rings can naturally form outside the SMBH sphere of influence.Comment: Accepted for publication in ApJ. 12 pages, 6 figures, 3 tables. Comments welcom