An Underlying Theory for Gravity

A new direction to understand gravity has recently been explored by considering classical gravity to be a derived interaction from an underlying theory. This underlying theory would involve new degrees of freedom at a deeper level and it would be structurally different from classical gravitation. It may conceivably be a quantum theory or a non-quantum theory. The relation between this underlying theory and Einstein's gravity is similar to the connection between statistical mechanics and thermodynamics. We discuss the apparent lack of evidence of any quantum nature of gravity in this context.Comment: Contributed paper to VIIth International Conference on Gravitation and Cosmology, 14 - 19 December, 2011 GOA, INDIA. 4 page

L2L_2 boosting in kernel regression

In this paper, we investigate the theoretical and empirical properties of $L_2$ boosting with kernel regression estimates as weak learners. We show that each step of $L_2$ boosting reduces the bias of the estimate by two orders of magnitude, while it does not deteriorate the order of the variance. We illustrate the theoretical findings by some simulated examples. Also, we demonstrate that $L_2$ boosting is superior to the use of higher-order kernels, which is a well-known method of reducing the bias of the kernel estimate.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction

The electron addition spectrum A^+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r^2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A^+(k,omega) has a simple analytic form with contributions from one spinon, one holon and one antiholon all of which obey fractional statistics. The upper edge of A^+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.Comment: 5 pages, 1 figure, accepted for publication in Phys. Rev. Let

Collective Dynamics of Random Polyampholytes

We consider the Langevin dynamics of a semi-dilute system of chains which are random polyampholytes of average monomer charge $q$ and with a fluctuations in this charge of the size $Q^{-1}$ and with freely floating counter-ions in the surrounding. We cast the dynamics into the functional integral formalism and average over the quenched charge distribution in order to compute the dynamic structure factor and the effective collective potential matrix. The results are given for small charge fluctuations. In the limit of finite $q$ we then find that the scattering approaches the limit of polyelectrolyte solutions.Comment: 13 pages including 6 figures, submitted J. Chem. Phy

Characteristics of cloud-to-ground lightning activity over Seoul, South Korea in relation to an urban effect

Cloud-to-ground (CG) lightning flash data collected by the lightning detection network installed at the Korean Meteorological Administration (KMA) have been used to study the urban effect on lightning activity over and around Seoul, the largest metropolitan city of South Korea, for the period of 1989–1999. Negative and positive flash density and the percentage of positive flashes have been calculated. Calculation reveals that an enhancement of approximately 60% and 42% are observed, respectively, for negative and positive flash density over and downwind of the city. The percentage decrease of positive flashes occurs over and downwind of Seoul and the amount of decrease is nearly 20% compared to upwind values. The results are in good agreement with those obtained by Steiger et al. (2002) and Westcott (1995). CG lightning activities have also been considered in relation to annual averages of PM<sub>10</sub> (particulate matter with an aerodynamic diameter smaller than 10 μm) and sulphur dioxide (SO<sub>2</sub>) concentrations. Interesting results are found, indicating that the higher concentration of SO<sub>2</sub> contributes to the enhancement of CG lightning flashes. On the other hand, the contribution from PM<sub>10</sub> concentration has not appeared in this study to be as significant as SO<sub>2</sub> in the enhancement of CG lightning flashes. Correlation coefficients of 0.33 and 0.64 are found between the change in CG lightning flashes and the PM<sub>10</sub> and SO<sub>2</sub>, respectively, for upwind to downwind areas, suggesting a significant influence of the increased concentration of SO<sub>2</sub> on the enhancement of CG flashes

Size dependent line broadening in the emission spectra of single GaAs quantum dots: Impact of surface charges on spectral diffusion

Making use of droplet epitaxy, we systematically controlled the height of self-assembled GaAs quantum dots by more than one order of magnitude. The photoluminescence spectra of single quantum dots revealed the strong dependence of the spectral linewidth on the dot height. Tall dots with a height of ~30 nm showed broad spectral peaks with an average width as large as ~5 meV, but shallow dots with a height of ~2 nm showed resolution-limited spectral lines (<120 micro eV). The measured height dependence of the linewidths is in good agreement with Stark coefficients calculated for the experimental shape variation. We attribute the microscopic source of fluctuating electric fields to the random motion of surface charges at the vacuum-semiconductor interface. Our results offer guidelines for creating frequency-locked photon sources, which will serve as key devices for long-distance quantum key distribution.Comment: 6 pages, 6 figures; updated figs and their description

Combinatorial interpretation of Haldane-Wu fractional exclusion statistics

Assuming that the maximal allowed number of identical particles in state is an integer parameter, q, we derive the statistical weight and analyze the associated equation which defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q = 1 and q -> infinity (n_i/q -> 1), respectively. We show that the derived statistical weight provides a natural combinatorial interpretation of Haldane-Wu fractional exclusion statistics, and present exact solutions of the distribution equation.Comment: 8 pages, 2 eps-figure

Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel--Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes large data near a local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in [3], by E. Carneiro and the authors, that permits to study such propagation without additional conditions on the collision kernel. Finally, an $L^{p}$-stability result (with $1\leq p\leq\infty$) is presented assuming the aforementioned condition.Comment: 19 page