Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition

The distribution of the correlation dimension in a power law band random matrix model having critical, i.e. multifractal, eigenstates is numerically investigated. It is shown that their probability distribution function has a fixed point as the system size is varied exactly at a value obtained from the scaling properties of the typical value of the inverse participation number. Therefore the state-to-state fluctuation of the correlation dimension is tightly linked to the scaling properties of the joint probability distribution of the eigenstates.Comment: 4 pages, 5 figure

Hygroscopic properties of aerosol particles at high relative humidity and their diurnal variations in the North China Plain

The hygroscopic properties of submicron aerosol particles were determined at a suburban site (Wuqing) in the North China Plain among a cluster of cities during the period 17 July to 12 August, 2009. A High Humidity Tandem Differential Mobility Analyser (HH-TDMA) instrument was applied to measure the hygroscopic growth factor (GF) at 90%, 95% and 98.5% relative humidity (RH) for particles with dry diameters between 50 and 250 nm. The probability distribution of GF (GF-PDF) averaged over the period shows a distinct bimodal pattern, namely, a dominant more-hygroscopic (MH) group and a smaller nearly-hydrophobic (NH) group. The MH group particles were highly hygroscopic, and their GF was relatively constant during the period with average values of 1.54 ± 0.02, 1.81 ± 0.04 and 2.45 ± 0.07 at 90%, 95% and 98.5% RH (D0 = 100 nm), respectively. The NH group particles grew very slightly when exposed to high RH, with GF values of 1.08 ± 0.02, 1.13 ± 0.06 and 1.24 ± 0.13 respectively at 90%, 95% and 98.5% RH (D0 = 100 nm). The hygroscopic growth behaviours at different RHs were well represented by a single-parameter Köhler model. Thus, the calculation of GF as a function of RH and dry diameter could be facilitated by an empirical parameterization of κ as function of dry diameter. A strong diurnal pattern in number fraction of different hygroscopic groups was observed. The average number fraction of NH particles during the day was about 8%, while during the nighttime fractions up to 20% were reached. Correspondingly, the state of mixing in terms of water uptake varied significantly during a day. Simulations using a particle-resolved aerosol box model (PartMC-MOSAIC) suggest that the diurnal variations of aerosol hygroscopicity and mixing state were mainly caused by the evolution of the atmospheric mixing layer. The shallow nocturnal boundary layer during the night facilitated the accumulation of freshly emitted carbonaceous particles (mainly hydrophobic) near the surface while in the morning turbulence entrained the more aged and more hygroscopic particles from aloft and diluted the NH particles near the surface resulting in a decrease in the fraction of NH particles

Dimensionality dependence of the wave function statistics at the Anderson transition

The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.Comment: 4 pages, 4 figure

Wave function statistics and multifractality at the spin quantum Hall transition

The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $\Delta_q$ governing the scaling of moments $\sim L^{-qd-\Delta_q}$ with the system size $L$ and the spatial decay of wave function correlations. Two- and three-point correlation functions are calculated analytically by means of mapping onto the classical percolation, yielding the values $\Delta_2=-1/4$ and $\Delta_3=-3/4$. The multifractality spectrum obtained from numerical simulations is given with a good accuracy by the parabolic approximation $\Delta_q\simeq q(1-q)/8$ but shows detectable deviations. We also study statistics of the two-point conductance $g$, in particular, the spectrum of exponents $X_q$ characterizing the scaling of the moments $$. Relations between the spectra of critical exponents of wave functions ($\Delta_q$), conductances ($X_q$), and Green functions at the localization transition with a critical density of states are discussed.Comment: 16 pages, submitted to J. Phys. A, Special Issue on Random Matrix Theor

Heterogeneous freezing of droplets with immersed mineral dust particles – measurements and parameterization

During the measurement campaign FROST (FReezing Of duST), LACIS (Leipzig Aerosol Cloud Interaction Simulator) was used to investigate the immersion freezing behavior of size selected, coated and uncoated Arizona Test Dust (ATD) particles with a mobility diameter of 300 nm. Particles were coated with succinic acid (C4H6O4), sulfuric acid (H2SO4) and ammonium sulfate ((NH4)2SO4). Ice fractions at mixed-phase cloud temperatures ranging from 233.15 K to 239.15 K (±0.60 K) were determined for all types of particles. In this temperature range, pure ATD particles and those coated with C4H6O4 or small amounts of H2SO4 were found to be the most efficient ice nuclei (IN). ATD particles coated with (NH4)2SO4 were the most inefficient IN. Since the supercooled droplets were highly diluted before freezing occurred, a freezing point suppression due to the soluble material on the particles (and therefore in the droplets) cannot explain this observation. Therefore, it is reasonable to assume that the coatings lead to particle surface alterations which cause the differences in the IN abilities. Two different theoretical approaches based on the stochastic and the singular hypotheses were applied to clarify and parameterize the freezing behavior of the particles investigated. Both approaches describe the experimentally determined results, yielding parameters that can subsequently be used to compare our results to those from other studies. However, we cannot clarify at the current state which of the two approaches correctly describes the investigated immersion freezing process. But both approaches confirm the assumption that the coatings lead to particle surface modifications lowering the nucleation efficiency. The stochastic approach interprets the reduction in nucleation rate from coating as primarily due to an increase in the thermodynamic barrier for ice formation (i.e., changes in interfacial free energies). The singular approach interprets the reduction as resulting from a reduced surface density of active sites

Improved Measurement of the K+ to pi+ nu nubar Branching Ratio

An additional event near the upper kinematic limit for K+ to pi+ nu nubar has been observed by Experiment E949 at Brookhaven National Laboratory. Combining previously reported and new data, the branching ratio is B(K+ to pi+ nu nubar)= 1.47 (+1.30, - 0.89) x 10-10 based on three events observed in the pion momentum region 211<P<229 MeV/c. At the measured central value of the branching ratio, the additional event had a signal-to-background ratio of 0.9

Measurement of Direct Photon Emission in K^+ -> pi^+ pi^0 gamma Decay

We have performed a measurement of the K^+ -> pi^+ pi^0 gamma decay and have observed 2 X 10^4 events. The best fit to the decay spectrum gives a branching ratio for direct photon emission of (4.7\pm0.8\pm0.3) X 10^{-6} in the pi^+ kinetic energy region of 55 to 90 MeV and requires no component due to interference with inner bremsstrahlung.Comment: 9 pages, 3 figures. To be submitted to PR

Aerosol optical properties in the North China Plain during HaChi campaign: An in-situ optical closure study

The largest uncertainty in the estimation of climate forcing stems from atmospheric aerosols. In early spring and summer of 2009, two periods of in-situ measurements on aerosol physical and chemical properties were conducted within the HaChi (Haze in China) project at Wuqing, a town between Beijing and Tianjin in the North China Plain (NCP). Aerosol optical properties, including the scattering coefficient (σsp), the hemispheric back scattering coefficient (σbsp), the absorption coefficient (σap), as well as the single scattering albedo (ω), are presented. The diurnal and seasonal variations are analyzed together with meteorology and satellite data. The mean values of σsp, 550 nm of the dry aerosol in spring and summer are 280±253 and 379±251 Mm−1, respectively. The average σap for the two periods is respectively 47±38 and 43±27 Mm−1. The mean values of ω at the wavelength of 637 nm are 0.82±0.05 and 0.86±0.05 for spring and summer, respectively. The relative high levels of σsp and σbsp are representative of the regional aerosol pollution in the NCP. Pronounced diurnal cycle of $σsp, σap and ω are found, mainly influenced by the evolution of boundary layer and the accumulation of local emissions during nighttime. The pollutants transported from the southwest of the NCP are more significant than that from the two megacities, Beijing and Tianjin, in both spring and summer. An optical closure experiment is conducted to better understand the uncertainties of the measurements. Good correlations (R>0.98) are found between the values measured by the nephelometer and the values calculated with a modified Mie model. The Monte Carlo simulation shows an uncertainty of about 30 % for the calculations. Considering all possible uncertainties of measurements, calculated σsp and σbsp agree well with the measured values, indicating a stable performance of instruments and thus reliable aerosol optical data

Further Evidence for the Decay K+ to pi+ neutrino-antineutrino

Additional evidence for the rare kaon decay K+ to pi+ neutrino-antineutrino has been found in a new data set with comparable sensitivity to the previously reported result. One new event was observed in the pion momentum region examined, 211<P<229 MeV/c, bringing the total for the combined data set to two. Including all data taken, the backgrounds were estimated to contribute 0.15 pm 0.05 events. The branching ratio is B=1.57^{+1.75}_{-0.82} 10^{-10}.Comment: 10 pages, 2 figure

Fractal superconductivity near localization threshold

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model. Our theoretical analysis is based on the analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems. We identify three distinct phases: 'critical' superconductive state formed at $E_F=E_c$, superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at $E_F$ still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap $\Delta$, that is due to many-body correlations and a new "pseudogap" energy scale $\Delta_P$ which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive $T_c$. Two gap nature of the "pseudo-gaped superconductor" is shown to lead to a number of unusual physical properties.Comment: 110 pages, 39 figures. The revised version corrects a number of typos, adds references and discussion of recent result