The local adsorption site of methylthiolate on Au(1 1 1): Bridge or atop?

Measurements of the local adsorption geometry of the S head-group atom in the Au(1 1 1)(√3 × √3)R30°–CH3S surface have been made using normal incidence X-ray standing waves (NIXSW) and S 1s scanned-energy mode photoelectron diffraction on the same surface preparations. The results confirm that the local adsorption site is atop an Au atom in a bulk-continuation site with a S–Au bondlength of 2.42 ± 0.02 Å, and that there can be no significant fraction of coadsorbed bridging species as recently proposed in a combined molecular dynamics/experimental study by Mazzarello et al. [R. Mazzarello, A. Cossaro, A. Verdini, R. Rousseau, L. Casalis, M.F. Danisman, L. Floreano, S. Scandolo, A. Morgante, G. Scoles, Phys. Rev. Lett. 98 (2007) 016102]. The results do not, however, clearly distinguish the different local reconstruction (adatom) models proposed for this surface

Logarithmic delocalization of end spins in the S=3/2 antiferromagnetic Heisenberg chain

Using the DMRG method we calculate the surface spin correlation function, $C_L(l)=$, in the spin $S=3/2$ antiferromagnetic Heisenberg chain. For comparison we also investigate the $S=1/2$ chain with S=1 impurity end spins and the S=1 chain. In the half-integer spin models the end-to-end correlations are found to decay to zero logarithmically, $C_L(1)\sim (\log L)^{-2d}$, with $d=0.13(2)$. We find no surface order, in clear contrast with the behavior of the S=1 chain, where exponentially localized end spins induce finite surface correlations. The lack of surface order implies that end spins do not exist in the strict sense. However, the system possesses a logarithmically weakly delocalizing boundary excitation, which, for any chain lengths attainable numerically or even experimentally, creates the illusion of an end spin. This mode is responsible for the first gap, which vanishes asymptotically as $\Delta_1 \approx (\pi v_S d)/(L\ln L)$, where $v_S$ is the sound velocity and $d$ is the logarithmic decay exponent. For the half-integer spin models our results on the surface correlations and on the first gap support universality. Those for the second gap are less conclusive, due to strong higher-order corrections.Comment: 10 pages, 8 figure

On certain diophantine equations of diagonal type

In this note we consider Diophantine equations of the form \begin{equation*} a(x^p-y^q) = b(z^r-w^s), \quad \mbox{where}\quad \frac{1}{p}+\frac{1}{q}+\frac{1}{r}+\frac{1}{s}=1, \end{equation*} with even positive integers $p,q,r,s$. We show that in each case the set of rational points on the underlying surface is dense in the Zariski topology. For the surface with $(p,q,r,s)=(2,6,6,6)$ we prove density of rational points in the Euclidean topology. Moreover, in this case we construct infinitely many parametric solutions in coprime polynomials. The same result is true for $(p,q,r,s)\in\{(2,4,8,8), (2,8,4,8)\}$. In the case $(p,q,r,s)=(4,4,4,4)$, we present some new parametric solutions of the equation $x^4-y^4=4(z^4-w^4)$.Comment: 16 pages, revised version will appear in the Journal of Number Theor