Linear and Non Linear Effects on the Newtonian Gravitational Constant as deduced from the Torsion Balance

The Newtonian gravitational constant has still 150 parts per million of uncertainty. This paper examines the linear and nonlinear equations governing the rotational dynamics of the torsion gravitational balance. A nonlinear effect modifying the oscillation period of the torsion gravitational balance is carefully explored.Comment: 11 pages, 2 figure

Bound States and Critical Behavior of the Yukawa Potential

We investigate the bound states of the Yukawa potential $V(r)=-\lambda \exp(-\alpha r)/ r$, using different algorithms: solving the Schr\"odinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical $\alpha=\alpha_C$, above which no bound state exists. We study the relation between $\alpha_C$ and $\lambda$ for various angular momentum quantum number $l$, and find in atomic units, $\alpha_{C}(l)= \lambda [A_{1} \exp(-l/ B_{1})+ A_{2} \exp(-l/ B_{2})]$, with $A_1=1.020(18)$, $B_1=0.443(14)$, $A_2=0.170(17)$, and $B_2=2.490(180)$.Comment: 15 pages, 12 figures, 5 tables. Version to appear in Sciences in China

On Black Hole Stability in Critical Gravities

We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive spin-2 modes are replaced by the log modes. There always exist certain linear combination of massless and log modes that has negative energy. Thus the stability of the black holes requires that the log modes to be truncated out by the boundary condition.Comment: 16 pages, minor corrections, further comments and references adde

Theoretical modeling of spatial and temperature dependent exciton energy in coupled quantum wells

Motivated by a recent experiment of spatial and temperature dependent average exciton energy distribution in coupled quantum wells [S. Yang \textit{et al.}, Phys. Rev. B \textbf{75}, 033311 (2007)], we investigate the nature of the interactions in indirect excitons. Based on the uncertainty principle, along with a temperature and energy dependent distribution which includes both population and recombination effects, we show that the interplay between an attractive two-body interaction and a repulsive three-body interaction can lead to a natural and good account for the nonmonotonic temperature dependence of the average exciton energy. Moreover, exciton energy maxima are shown to locate at the brightest regions, in agreement with the recent experiments. Our results provide an alternative way for understanding the underlying physics of the exciton dynamics in coupled quantum wells.Comment: 8 pages, 5 figure