Optical conductivity of a granular metal at not very low temperatures

We study the finite-temperature optical conductivity, sigma(omega,T), of a granular metal using a simple model consisting of a array of spherical metallic grains. It is necessary to include quantum tunneling and Coulomb blockade effects to obtain the correct temperature dependence of sigma(omega, T), and to consider polarization oscillations to obtain the correct frequency dependence. We have therefore generalized the Ambegaokar-Eckern-Schoen (AES) model for granular metals to obtain an effective field theory incorporating the polarization fluctuations of the individual metallic grains. In contrast to the DC conductivity, which is determined by inter-grain charge transfer and obeys an Arrhenius law at low temperature, the AC conductivity is dominated by a resonance peak for intra-grain polarization oscillations, which has a power-law tail at low frequencies. More importantly, although the resonance frequency agrees with the classical prediction, the resonance width depends on intergrain quantum tunneling and Coulomb blockade parameters, in addition to the classical Drude relaxation within the grain. This additional damping is due to inelastic cotunneling of polarization fluctuations to neighbouring grains and it qualitatively differs from the DC conductivity in its temperature dependence quite unlike the expectation from Drude theory.Comment: Added figures, published version, 16 pages, REVTe

X-Ray Fluorescence Determination of Major Elements in Powder Chromium Ore Samples Prepared as Pressed Pellets

Предложен способ рентгенофлуоресцентного определения основных элементов (Cr, Fe, Si, Al, Mg), а также Mn и Ti в порошковых пробах хромовых руд. Измерения проводили на волноводисперсионном рентгенофлуоресцентном спектрометре S 4 Pioneer (Bruker AXS). Подготовка проб включала дополнительное измельчение порошков калибровочных образцов и анализируемых проб, которое обеспечивало размер частиц порошка менее 50 мкм. Для измерения готовили таблетки прессованием порошков на подложке из борной кислоты. Дополнительное измельчение позволило уменьшить влияние гранулометрического состава порошков на погрешность определения главных полезных компонентов: хрома и железа. В качестве калибровочной функции использовали эмпирическое уравнение Лукаса-Туса, имеющееся в опциях программного обеспечения спектрометра. Отклонения результатов рентгенофлуоресцентного анализа от результатов химического анализа с фотометрическим или атомно-абсорбционным окончанием для четырех контрольных проб составили менее: 0.34 % мас. для Cr2O3 (в диапазоне 18–56 % мас.), 0.16 % мас. для Fe2O3 (в диапазоне 10–26 % мас.), 0.29 % мас. для Al2O3 (в диапазоне 5–20 % мас.), 0.013 % мас. для MnO (в диапазоне 0.1–0.2 % мас.), 0.03 % мас. для TiO2 (в диапазоне 0.09–0.67 % мас.). Для MgO (в диапазоне 14–32 % мас.) и SiO2 (в диапазоне 2–22 % мас.) погрешность определения может быть более 1 % мас., что превышает допустимую для количественного определенияX‑ray fluorescence techniques is proposed for the determination of the main elements (Cr, Fe, Si, Al, Mg), as well as Mn and Ti, in powder samples of chromium ores. The measurements were carried out using wavelength- dispersive X‑ray fluorescence spectrometer S 4 Pioneer (Bruker AXS). Sample preparation included additional grinding of calibration and analyzed samples, which ensured a powder particle size of less than 50 μm. Pellets were prepared for measurements by pressing powders on a boric acid substrate. Additional grinding made it possible to reduce the influence of the granulometric composition of powders on the error in determining the main useful components: chromium and iron. The available in the software options of the spectrometer empirical Lucas- Tooth equation was used as a calibration function. Deviations between X‑ray fluorescence and chemical analysis (photometry or atomic absorption spectrometry) results for four test samples were less than: 0.34 wt.% for Cr2O3 (in the range of 18–56 wt.%), 0.16 wt.% for Fe2O3 (in the range of 10–26 wt.%), 0.29 wt.% for Al2O3 (in the range of 5–20 wt.%), 0.013 wt.% for MnO (in the range of 0.1–0.2 wt.%), 0.03 wt.% for TiO2 (in the range of 0.09–0.67 wt.%). For the MgO (in the range of 14–32 wt.%) and SiO2, (in the range of 2–22 wt.%), the error can be more than 1 wt.% that exceeds the allowable error for quantitative determinatio

The renormalization group for interacting fermions: from Fermi liquids to quantum dots

The renormalization group approach as developed by the author for Fermi liquids is applied to clean Fermi liquids and ballistic quantum dots. In the former case Landau theory is shown to be a fixed point and in the latter the Universal Hamiltonian is shown to be a fixed point for weak coupling. The strong coupling phase is analyzed using large N and Random Matrix methods.Comment: Lectures given at the Fifteenth Chris Engelbrecht Summer School South Africa, January 2004. 6 eps figs and springer style file (svmult