The connection between entropy and the absorption spectra of Schwarzschild black holes for light and massless scalar fields

We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value $c$, for wavelengths larger than $R_{s}$, in the vicinity of $R_{s}$. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent 'particle' description fails, and the wave nature becomes apparent.Comment: 14 Pages, 4 figures. Accepted for publication in the Journal Entrop

How is silicic acid transported in plants?

Plants accumulate silicon in their tissues as amorphous silica. The form of silicon taken up by plants is silicic acid, a neutral molecule that passes through membrane channels with water. After seminal work on rice identified an aquaporin that appeared to mediate the passage of silicic acid, several papers followed and classified similar channels (referred to as “transporters”) in a number of plant species. These channels have been described as essential for silicon uptake and specific for the metalloid. Herein, we critically review the published data on the characterisation of one channel in particular, Lsi1, and identify possible caveats in results and limitations in methods used. Our analysis does not support the suggestion that the identified channels are specific for silicic acid. Computational analyses of the size of the Lsi1 pore additionally suggest that it may not play a significant role in mediating the movement of silicic acid in planta. We suggest that to avoid further confusion, channels currently implicated in the transport of silicic acid in planta are not referred to as silicon-specific transporters. Future research including the use of molecular dynamics simulations will enable the unequivocal identification of channels involved in silicon transport in plants

On the Incidence of C IV Absorbers Along the Sightlines to Gamma-Ray Bursts

We report on the statistics of strong (W_r > 0.15 A) C IV absorbers at z=1.5-3.5 toward high-redshift gamma-ray bursts (GRBs). In contrast with a recent survey for strong Mg II absorption systems at z < 2, we find that the number of C IV absorbers per unit redshift dN/dz does not show a significant deviation from previous surveys using quasi-stellar objects (QSOs) as background sources. We find that the number density of C IV toward GRBs is dN/dz(z~1.5)= 2.2 +2.8/-1.4, dN/dz(z~2.5)= 2.3 +1.8/-1.1 and dN/dz(z~3.5)= 1.1 +2.6/-0.9. These numbers are consistent with previous C IV surveys using QSO spectra. Binning the entire dataset, we set a 95% c.l. upper limit to the excess of C IV absorbers along GRB sightlines at twice the incidence observed along QSO sightlines. Furthermore, the distribution of equivalent widths of the GRB and QSO samples are consistent with being drawn from the same parent population. Although the results for Mg II and C IV absorbers along GRB sightlines appear to contradict one another, we note that the surveys are nearly disjoint: the C IV survey corresponds to higher redshift and more highly ionized gas than the Mg II survey. Nevertheless, analysis on larger statistical samples may constrain properties of the galaxies hosting these metals (e.g. mass, dust content) and/or the coherence-length of the gas giving rise to the metal-line absorption.Comment: Accepted version (for publication in ApJ), results unchanged, 18 pages, 3 tables, 5 figure

Modelling Defect Cavities Formed in Inverse Three-Dimensional Rod-Connected Diamond Photonic Crystals

Defect cavities in 3D photonic crystal can trap and store light in the smallest volumes allowable in dielectric materials, enhancing non-linearities and cavity QED effects. Here, we study inverse rod-connected diamond (RCD) crystals containing point defect cavities using plane-wave expansion and finite-difference time domain methods. By optimizing the dimensions of the crystal, wide photonic band gaps are obtained. Mid-bandgap resonances can then be engineered by introducing point defects in the crystal. We investigate a variety of single spherical defects at different locations in the unit cell focusing on high-refractive-index contrast (3.3:1) inverse RCD structures; quality factors (Q-factors) and mode volumes of the resonant cavity modes are calculated. By choosing a symmetric arrangement, consisting of a single sphere defect located at the center of a tetrahedral arrangement, mode volumes < 0.06 cubic wavelengths are obtained, a record for high index cavities.Comment: 7 pages, 8 figure

Non-equilibrium tunneling into general quantum Hall edge states

In this paper we formulate the theory of tunneling into general Abelian fractional quantum Hall edge states. In contrast to the simple Laughlin states, a number of charge transfer processes must be accounted for. Nonetheless, it is possible to identify a unique value corresponding to dissipationless transport as the asymptotic large-$V$ conductance through a tunneling junction, and find fixed points (CFT boundary conditions) corresponding to this value. The symmetries of a given edge tunneling problem determine the appropriate boundary condition, and the boundary condition determines the strong-coupling operator content and current noise.Comment: 6 pages, 3 figures; published versio

GU Boo: A New 0.6 Msun Detached Eclipsing Binary

We have found a new low-mass, double-lined, detached eclipsing binary, GU Boo, among a sample of new variables from the ROTSE-I database. The binary has an orbital period of 0.488728 +/- 0.000002 days, and estimated apparent magnitudes Vrotse = 13.7 and I = 11.8. Our analysis of the light and radial velocity curves of the system yields individual masses and radii of M1= 0.610 +/- 0.007 Msun, M2 = 0.599 +/- 0.006 Msun, R1= 0.623 +/- 0.016 Rsun, R2= 0.620 +/- 0.020 Rsun. The stars in GU Boo are therefore very similar to the components of the eclipsing binary YY Gem. For this study we have adopted a mean effective temperature for the binary of Teff = 3870 +/- 130 K. Based on its space velocities we suggest that GU Boo is a main sequence binary, possibly with an age of several Gyr. The metallicity of the binary is not well constrained at this point but we speculate that it should not be very different from solar. We have compared the physical parameters of GU Boo with current low-mass stellar models, where we accounted for uncertainties in age and metallicity by considering a wide range of values for those parameters. Our comparisons reveal that all the models underestimate the radii of the components of GU Boo by at least 10-15%. This result is in agreement with the recent studies of YY Gem and CU Cnc.Comment: 41 pages, 10 figures, 11 tables; accepted by Ap

Infinite Symmetry in the Fractional Quantum Hall Effect

We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for the fractional quantum Hall effect such that the negative modes annihilate the Laughlin wave functions. This generalization has a nice interpretation in Jain's composite fermion theory. Furthermore, for these models we have calculated the wave functions of the edge excitations viewing them as area preserving deformations of an incompressible quantum droplet, and have shown that the ${\cal W}_{1+\infty}$ is the underlying symmetry of the edge excitations in the fractional quantum Hall effect. Finally, we have applied this method to more general wave functions.Comment: 15pp. LaTeX, BONN-HE-93-2

From the Chern-Simons theory for the fractional quantum Hall effect to the Luttinger model of its edges

The chiral Luttinger model for the edges of the fractional quantum Hall effect is obtained as the low energy limit of the Chern-Simons theory for the two dimensional system. In particular we recover the Kac-Moody algebra for the creation and annihilation operators of the edge density waves and the bosonization formula for the electronic operator at the edge.Comment: 4 pages, LaTeX, 1 Postscript figure include