Connectivity and a Problem of Formal Geometry

Let $P=\mathbb P^m(e)\times\mathbb P^n(h)$ be a product of weighted projective spaces, and let $\Delta_P$ be the diagonal of $P\times P$. We prove an algebraization result for formal-rational functions on certain closed subvarieties $X$ of $P\times P$ along the intersection $X\cap\Delta_P$.Comment: 9 pages, to appear in the Proceedings volume "Experimental and Theoretical Methods in Algebra, Geometry and Topology", series Springer Proceedings in Mathematics & Statistic

Mixing of two-electron spin states in a semiconductor quantum dot

We show that the low lying spin states of two electrons in a semiconductor quantum dot can be strongly mixed by electron-electron asymmetric exchange. This mixing is generated by the coupling of electron spin to its orbital motion and to the relative orbital motion of the two electrons. The asymmetric exchange can be as large as 50% of the isotropic exchange, even for cylindrical quantum dots. The resulting spin mixing contributes to understanding spin dynamics in quantum dots, including light polarization reversal

Formal properties in small codimension

In this note we extend connectedness results to formal properties of inverse images under proper maps of Schubert varieties and of the diagonal in products of projective rational homogeneous spaces

Polarized fine structure in the excitation spectrum of a negatively charged quantum dot

We report polarized photoluminescence excitation spectroscopy of the negative trion in single charge tunable InAs/GaAs quantum dots. The spectrum exhibits a p-shell resonance with polarized fine structure arising from the direct excitation of the electron spin triplet states. The energy splitting arises from the axially symmetric electron-hole exchange interaction. The magnitude and sign of the polarization are understood from the spin character of the triplet states and a small amount of quantum dot asymmetry, which mixes the wavefunctions through asymmetric e-e and e-h exchange interactions

Energetics and Vibrational States for Hydrogen on Pt(111)

We present a combination of theoretical calculations and experiments for the low-lying vibrational excitations of H and D atoms adsorbed on the Pt(111) surface. The vibrational band states are calculated based on the full three-dimensional adiabatic potential energy surface obtained from first principles calculations. For coverages less than three quarters of a monolayer, the observed experimental high-resolution electron peaks at 31 and 68meV are in excellent agreement with the theoretical transitions between selected bands. Our results convincingly demonstrate the need to go beyond the local harmonic oscillator picture to understand the dynamics of this system.Comment: In press at Phys. Rev. Lett - to appear in April 200

Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Does inequality erode generalized trust? Evidence from Romanian youths

Generalized trust is a critical component of liberal democratic citizenship. We evaluate the extent to which exposure to socioeconomic inequality erodes trust among Romanian youths. Using national survey data of Romanian eighth-grade and high school students, we evaluate this effect as a product of socioeconomic diversity within the classroom, controlling for the social status of the students as well as socioeconomic inequality within the community where the school is located. Our analysis shows that generalized trust is higher for students in higher grades. However, despite this maturing effect, students exposed to greater levels of socioeconomic diversity have significantly lower levels of trust. The effect is particularly acute for students in the ninth grade. This finding holds when controlling for socioeconomic diversity and polarization in the community. The result reinforces the idea that generalized trust develops early in one’s life and is quite stable, although a major life transformation, such as entering high school, may alter trust depending on the social context