Who Shrunk China? Puzzles in the Measurement of Real GDP

The latest World Bank estimates of real GDP per capita for China are significantly lower than previous ones. We review possible sources of this puzzle and conclude that it reflects a combination of factors, including substitution bias in consumption, reliance on urban prices which we estimate are higher than rural ones, and the use of an expenditure-weighted rather than an output-weighted measure of GDP. Taking all these together, we estimate that real per-capita GDP in China was 50% higher relative to the U.S. in 2005 than the World Bank estimates.

Percolation in random environment

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are non-universal, whereas for strong enough disorder the system scales into an {\it infinite randomness fixed point} in which the critical exponents are exactly known.Comment: 8 pages, 7 figure

Determination of Heavy Metals in Hoplobatrachus occipitalis (Crowned Bullfrogs) and Water from Some Reservoirs in Kadawa Irrigation Project Kano, Nigeria

This study was carried out to evaluate the concentrations of heavy metals (Cd, Cu, Mn, Pb, and Zn) in water and crowned bullfrog (Hoplobatrachus occipitalis) organs/parts (muscle, liver, leg, lung and trunk) from Kadawa irrigation project, Kano State, Nigeria. Atomic Absorption Spectroscopy was carried out using Atomic Absorption Spectrometer (AAS) Buck Scientific VGP-210 model (2008). The mean concentration of heavy metals in water samples were 0.11 mg/L, 0.18 mg/L, 0.26 mg/L, and 3.65 mg/L for Cu, Mn, Pb and Zn respectively. The sequence of metal accumulation in all the organs was Zn > Pb > Mn > Cu. The highest concentration of Zn (77.38 mg/kg), Pb (1.81 mg/kg) and Mn (0.68 mg/kg) were found in the lung while Cu (0.07 mg/kg) was deposited more in the liver. Cadmium was notdetected in all the samples analysed. Zinc and lead were the most accumulated metals in all the organs/parts with the range of 77.38 mg/kg - 18.10 mg/kg and 1.81 mg/kg - 0.13 mg/kg respectively. The highest accumulation of metals was found in the lung and liver. The organ/parts accumulation pattern was: lung > liver > trunk > muscle > leg for Zn, Pb and Mn, while liver > lung > trunk > muscle > leg was for Cu. Lung and liver have the highest bioaccumulation of heavy metals while the leg and muscle bioaccumulated the least heavy metals. Hence the water, liver and lung of H. occipitallis are unsafe for consumption, and therefore posed a threat to public health. Farmers should be trained on proper usage of agrochemical.Keywords: Heavy Metals, Crowned Bullfrog, Hoplobatrachus occipitalis, Kadawa, Bioaccumulatio

Griffiths Effects in Random Heisenberg Antiferromagnetic S=1 Chains

I consider the effects of enforced dimerization on random Heisenberg antiferromagnetic S=1 chains. I argue for the existence of novel Griffiths phases characterized by {\em two independent dynamical exponents} that vary continuously in these phases; one of the exponents controls the density of spin-1/2 degrees of freedom in the low-energy effective Hamiltonian, while the other controls the corresponding density of spin-1 degrees of freedom. Moreover, in one of these Griffiths phases, the system has very different low temperature behavior in two different parts of the phase which are separated from each other by a sharply defined crossover line; on one side of this crossover line, the system `looks' like a S=1 chain at low energies, while on the other side, it is best thought of as a $S=1/2$ chain. A strong-disorder RG analysis makes it possible to analytically obtain detailed information about the low temperature behavior of physical observables such as the susceptibility and the specific heat, as well as identify an experimentally accessible signature of this novel crossover.Comment: 16 pages, two-column PRB format; 5 figure

Superradiant and Aharonov-Bohm effect for the quantum ring exciton

The Aharonov-Bohm and superradiant effect on the redaitive decay rate of an exciton in a quantum ring is studied. With the increasing of ring radius, the exciton decay rate is enhanced by superradiance, while the amplitude of AB oscillation is decreased. The competition between these two effects is shown explicitly and may be observable in time-resolved exeriments.Comment: 4 pages, 2 figures, to appear in Solid State Communications (2004

Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains

Random spin-3/2 antiferromagnetic Heisenberg chains are investigated using an asymptotically exact renormalization group. Randomness is found to induce a quantum phase transition between two random-singlet phases. In the strong randomness phase the effective spins at low energies are S_eff=3/2, while in the weak randomness phase the effective spins are S_eff=1/2. Separating them is a quantum critical point near which there is a non-trivial mixture of S=1/2, S=1, and S=3/2 effective spins at low temperatures.Comment: 4 pages, 3 figures. Typos correcte

Spin-3/2 random quantum antiferromagnetic chains

We use a modified perturbative renormalization group approach to study the random quantum antiferromagnetic spin-3/2 chain. We find that in the case of rectangular distributions there is a quantum Griffiths phase and we obtain the dynamical critical exponent $Z$ as a function of disorder. Only in the case of extreme disorder, characterized by a power law distribution of exchange couplings, we find evidence that a random singlet phase could be reached. We discuss the differences between our results and those obtained by other approaches.Comment: 4 page

B_c meson rare decays in the light-cone quark model

We investigate the rare decays $B_c \rightarrow D_s(1968) \ell \bar{\ell}$ and $B_c\rightarrow D_s^*(2317) \ell \bar{\ell}$ in the framework of the light-cone quark model (LCQM). The transition form factors are calculated in the space-like region and then analytically continued to the time-like region via exponential parametrization. The branching ratios and longitudinal lepton polarization asymmetries (LPAs) for the two decays are given and compared with each other. The results are helpful to investigating the structure of $B_c$ meson and to testing the unitarity of CKM quark mixing matrix. All these results can be tested in the future experiments at the LHC.Comment: 9 pages, 11 figures, version accepted for publication in EPJ

Smeared phase transition in a three-dimensional Ising model with planar defects: Monte-Carlo simulations

We present results of large-scale Monte Carlo simulations for a three-dimensional Ising model with short range interactions and planar defects, i.e., disorder perfectly correlated in two dimensions. We show that the phase transition in this system is smeared, i.e., there is no single critical temperature, but different parts of the system order at different temperatures. This is caused by effects similar to but stronger than Griffiths phenomena. In an infinite-size sample there is an exponentially small but finite probability to find an arbitrary large region devoid of impurities. Such a rare region can develop true long-range order while the bulk system is still in the disordered phase. We compute the thermodynamic magnetization and its finite-size effects, the local magnetization, and the probability distribution of the ordering temperatures for different samples. Our Monte-Carlo results are in good agreement with a recent theory based on extremal statistics.Comment: 9 pages, 6 eps figures, final version as publishe

Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet

We examine the spin-$S$ quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is accessed by generalizing to $SU(M)$ symmetry and studying the large $M$ limit. For large $S$ the ground state is a spin-glass, while quantum fluctuations produce a spin-fluid state for small $S$. The spin-fluid phase is found to be generically gapless - the average, zero temperature, local dynamic spin-susceptibility obeys \bar{\chi} (\omega ) \sim \log(1/|\omega|) + i (\pi/2) \mbox{sgn} (\omega) at low frequencies. This form is identical to the phenomenological `marginal' spectrum proposed by Varma {\em et. al.\/} for the doped cuprates.Comment: 13 pages, REVTEX, 2 figures available by request from [email protected]