Statistical fluctuations of the parametric derivative of the transmission and reflection coefficients in absorbing chaotic cavities

Motivated by recent theoretical and experimental works, we study the statistical fluctuations of the parametric derivative of the transmission T and reflection R coefficients in ballistic chaotic cavities in the presence of absorption. Analytical results for the variance of the parametric derivative of T and R, with and without time-reversal symmetry, are obtained for both asymmetric and left-right symmetric cavities. These results are valid for arbitrary number of channels, in completely agreement with the one channel case in the absence of absorption studied in the literature.Comment: Modified version as accepted in PR

Uji Efektivitas Pupuk Organonitrofos Dan Kombinasinya Dengan Pupuk Anorganik Terhadap Serapan Hara Dan Produksi Tanaman Jagung (Zea Mays L.) Pada Musim Tanam Ke Dua Di Tanah Ultisols Gedong Meneng

Pupuk Organonitrofos merupakan pupuk organik baru yang terbuat dari pencampuran kotoran sapi dengan batuan fosfat alam yang diperkaya mikroorganisme penambat N dan pelarut P. Penelitian ini bertujuan untuk mengetahui efektivitas pupuk Organonitrofos dan kombinasinya dengan pupuk anorganik terhadap pertumbuhan, serapan hara, dan produksi tanaman jagung. Penelitian ini menggunakan Rancangan Acak Kelompok (RAK) terdiri dari 6 perlakuan yaitu A (kontrol), B (900 kg urea ha-1, 250 kg SP-36 ha-1, 250 kg KCl ha-1), C (600 kg urea ha-1, 150 kg SP-36 ha-1, 150 kg KCl ha-1, 500 kg Organonitrofos ha-1), D (150 kg urea ha-1, 50 kg SP-36 ha-1, 100 kg KCl ha-1, 1.000 kg Organonitrofos ha-1), E (100 kg urea ha-1, 50 kg SP-36 ha-1, 100 kg KCl ha-1, 2.000 kg Organonitrofos ha-1), dan F (3.000 kg Organonitrofos ha-1) dengan 3 ulangan. Hasil penelitian menunjukkan bahwa pupuk Organonitrofos mampu mengurangi penggunaan pupuk anorganik. Berdasarkan perhitungan standar deviasi kombinasi antara pupuk anorganik dan Organonitrofos pada perlakuan D dengan dosis 150 kg urea ha-1, 50 kg SP36 ha-1, 100 kg KCl ha-1, 1.000 kg Organonitrofos ha-1 menunjukkan hasil pertumbuhan, produksi, serta serapan hara N, P, dan K total tertinggi. Perlakuan D juga paling efektif terhadap biomass total tanaman jagung berdasarkan perhitungan Relative Agronomic Effectiveness yaitu sebesar 125,33 %. Serapan hara N, P, dan K berkorelasi dengan tinggi tanaman, bobot pipilan kering serta bobot berangkasan tanaman, kecuali antara serapan P dengan tinggi tanaman

Composite fermion wave functions as conformal field theory correlators

It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function at filling factor $\nu=1/m$ ($m$ odd) and its quasiholes, and the Pfaffian wave function at $\nu=1/2$ and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at $\nu=1/m$ are created by inserting anyonic vertex operators, $P_{\frac{1}{m}}(z)$, that replace a subset of the electron operators in the correlator. The one-quasiparticle wave function is identical to the corresponding CF wave function, and the two-quasiparticle wave function has correct fractional charge and statistics and is numerically almost identical to the corresponding CF wave function. We further show how to exactly represent the CF wavefunctions in the Jain series $\nu = s/(2sp+1)$ as the CFT correlators of a new type of fermionic vertex operators, $V_{p,n}(z)$, constructed from $n$ free compactified bosons; these operators provide the CFT representation of composite fermions carrying $2p$ flux quanta in the $n^{\rm th}$ CF Landau level. We also construct the corresponding quasiparticle- and quasihole operators and argue that they have the expected fractional charge and statistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs that describe the bulk wave functions are identical to those given by Wen's general classification of quantum Hall states in terms of $K$-matrices and $l$- and $t$-vectors, and we propose that to be generally true. Our results suggest a general procedure for constructing quasiparticle wave functions for other fractional Hall states, as well as for constructing ground states at filling fractions not contained in the principal Jain series.Comment: 26 pages, 3 figure

Random Matrix Theory Analysis of Cross Correlations in Financial Markets

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of ``level repulsion'' in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure

Finding the Pion in the Chiral Random Matrix Vacuum

The existence of a Goldstone boson is demonstrated in chiral random matrix theory. After determining the effective coupling and calculating the scalar and pseudoscalar propagators, a random phase approximation summation reveals the massless pion and massive sigma modes expected whenever chiral symmetry is spontaneously broken.Comment: 3 pages, 1 figure, revte

Solitons and Quasielectrons in the Quantum Hall Matrix Model

We show how to incorporate fractionally charged quasielectrons in the finite quantum Hall matrix model.The quasielectrons emerge as combinations of BPS solitons and quasiholes in a finite matrix version of the noncommutative $\phi^4$ theory coupled to a noncommutative Chern-Simons gauge field. We also discuss how to properly define the charge density in the classical matrix model, and calculate density profiles for droplets, quasiholes and quasielectrons.Comment: 15 pages, 9 figure

Modelling gravity on a hyper-cubic lattice

We present an elegant and simple dynamical model of symmetric, non-degenerate (n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic lattice with nearest-neighbor interactions. We show how this model is related to General Relativity, and discuss multiple ways in which it can be useful for studying gravity, both classical and quantum. In particular, we show that the dynamics of the model when all matrices are close to the identity corresponds exactly to a finite-difference discretization of weak-field gravity in harmonic gauge. We also show that the action which defines the full dynamics of the model corresponds to the Einstein-Hilbert action to leading order in the lattice spacing, and use this observation to define a lattice analogue of the Ricci scalar and Einstein tensor. Finally, we perform a mean-field analysis of the statistical mechanics of this model.Comment: 5 page

Statistical wave scattering through classically chaotic cavities in the presence of surface absorption

We propose a model to describe the statistical properties of wave scattering through a classically chaotic cavity in the presence of surface absorption. Experimentally, surface absorption could be realized by attaching an "absorbing patch" to the inner wall of the cavity. In our model, the cavity is connected to the outside by a waveguide with N open modes (or channels), while an experimental patch is simulated by an "absorbing mirror" attached to the inside wall of the cavity; the mirror, consisting of a waveguide that supports Na channels, with absorption inside and a perfectly reflecting wall at its end, is described by a subunitary scattering matrix Sa. The number of channels Na, as a measure of the geometric cross section of the mirror, and the lack of unitarity of Sa as a measure of absorption, are under our control: these parameters have an important physical significance for real experiments. The absorption strength in the cavity is quantified by the trace of the lack of unitarity. The statistical distribution of the resulting S matrix for N=1 open channel and only one absorbing channel, Na =1, is solved analytically for the orthogonal and unitary universality classes, and the results are compared with those arising from numerical simulations. The relation with other models existing in the literature, in some of which absorption has a volumetric character, is also studied.Comment: 6 pages, 3 figures, submitted to Phys. Rev.

Exact Study of the Effect of Level Statistics in Ultrasmall Superconducting Grains

The reduced BCS model that is commonly used for ultrasmall superconducting grains has an exact solution worked out long ago by Richardson in the context of nuclear physics. We use it to check the quality of previous treatments of this model, and to investigate the effect of level statistics on pairing correlations. We find that the ground state energies are on average somewhat lower for systems with non-uniform than uniform level spacings, but both have an equally smooth crossover from the bulk to the few-electron regime. In the latter, statistical fluctuations in ground state energies strongly depend on the grain's electron number parity.Comment: 4 pages, 3 eps figs, RevTe

Factors influencing the catalytic oxidation of benzyl alcohol using supported phosphine-capped gold nanoparticles

Open Access Article. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.Two phosphine-stabilised gold clusters, Au101(PPh3)21Cl5 and Au9(PPh3)8(NO3)3, were deposited and activated on anatase TiO2 and fumed SiO2. These catalysts showed an almost complete oxidation of benzyl alcohol (>90%) within 3 hours at 80 °C and 3 bar O2 in methanol with a high substrate-to-metal molar ratio of 5800 and turn-over frequency of 0.65 s−1. Factors influencing catalytic activity were investigated, including metal–support interaction, effects of heat treatments, chemical composition of gold clusters, the size of gold nanoparticles and catalytic conditions. It was found that the anions present in gold clusters play a role in determining the catalytic activity in this reaction, with NO3− diminishing the catalytic activity. High catalytic activity was attributed to the formation of large gold nanoparticles (>2 nm) that coincides with partial removal of ligands which occurs during heat treatment and catalysis. Selectivity towards the formation of methyl benzoate can be tuned by selection of the reaction temperature. The catalysts were characterised using transmission electron microscopy, UV-vis diffuse reflectance spectroscopy and X-ray photoelectron spectroscopy