An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and $$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}}$$ are proved for the uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution function $\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta^3$. The first of these inequalities sharpens the best known version of the classical Berry--Esseen inequality since $0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the absolute constant in the classical Berry--Esseen inequality. The second inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051 which is strictly less than the least possible value of the absolute constant in the classical Berry--Esseen inequality. As a corollary, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined.Comment: 33 page

Temperature-driven single-valley Dirac fermions in HgTe quantum wells

We report on temperature-dependent magnetospectroscopy of two HgTe/CdHgTe quantum wells below and above the critical well thickness $d_c$. Our results, obtained in magnetic fields up to 16 T and temperature range from 2 K to 150 K, clearly indicate a change of the band-gap energy with temperature. The quantum well wider than $d_c$ evidences a temperature-driven transition from topological insulator to semiconductor phases. At the critical temperature of 90 K, the merging of inter- and intra-band transitions in weak magnetic fields clearly specifies the formation of gapless state, revealing the appearance of single-valley massless Dirac fermions with velocity of $5.6\times10^5$ m$\times$s$^{-1}$. For both quantum wells, the energies extracted from experimental data are in good agreement with calculations on the basis of the 8-band Kane Hamiltonian with temperature-dependent parameters.Comment: 5 pages, 3 figures and Supplemental Materials (4 pages

Ab initio optical properties of Si(100)

We compute the linear optical properties of different reconstructions of the clean and hydrogenated Si(100) surface within DFT-LDA, using norm-conserving pseudopotentials. The equilibrium atomic geometries of the surfaces, determined from self-consistent total energy calculations within the Car-Parrinello scheme, strongly influence Reflectance Anisotropy Spectra (RAS), showing differences between the p(2x2) and c(4x2)reconstructions. The Differential Reflectivity spectrum for the c(4x2) reconstruction shows a positive peak at energies < 1 eV, in agreement with experimental results.Comment: fig. 2 correcte

Anisotropic optical response of the diamond (111)-2x1 surface

The optical properties of the 2$\times$1 reconstruction of the diamond (111) surface are investigated. The electronic structure and optical properties of the surface are studied using a microscopic tight-binding approach. We calculate the dielectric response describing the surface region and investigate the origin of the electronic transitions involving surface and bulk states. A large anisotropy in the surface dielectric response appears as a consequence of the asymmetric reconstruction on the surface plane, which gives rise to the zigzag Pandey chains. The results are presented in terms of the reflectance anisotropy and electron energy loss spectra. While our results are in good agreement with available experimental data, additional experiments are proposed in order to unambiguously determine the surface electronic structure of this interesting surface.Comment: REVTEX manuscript with 6 postscript figures, all included in uu file. Also available at http://www.phy.ohiou.edu/~ulloa/ulloa.html Submitted to Phys. Rev.

Second harmonic generation in SiC polytypes

LMTO calculations are presented for the frequency dependent second harmonic generation (SHG) in the polytypes 2H, 4H, 6H, 15R and 3C of SiC. All independent tensor components are calculated. The spectral features and the ratios of the 333 to 311 tensorial components are studied as a function of the degree of hexagonality. The relationship to the linear optical response and the underlying band structure are investigated. SHG is suggested to be a sensitive tool for investigating the near band edge interband excitations.Comment: 12 pages, 10 figure