Theory of Néel and valence-bond solid phases on the kagome lattice of Zn paratacamite

Recently, neutron scattering data on powder samples of Zn paratacamite, ZnxCu4-x(OH)6Cl2, with small Zn concentration has been interpreted as evidence for valence-bond solid and Néel ordering [S.-H. Lee, Nat. Mater. 6, 853 (2007)10.1038/nmat1986]. We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence-bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and x-ray scattering experiments that can test our predictions.     

The Self-avoiding Walk Spanning a Strip

Populations of unicellular organisms that grow under constant environmental conditions are considered theoretically. The size distribution of these cells is calculated analytically, both for the usual process of binary division, in which one mother cell produces always two daughter cells, and for the more complex process of multiple division, in which one mother cell can produce 2 ⁿ daughter cells with n=1,2,3,… . The latter mode of division is inspired by the unicellular algae Chlamydomonas reinhardtii. The uniform response of the whole population to different environmental conditions is encoded in the individual rates of growth and division of the cells. The analytical treatment of the problem is based on size-dependent rules for cell growth and stochastic transition processes for cell division. The comparison between binary and multiple division shows that these different division processes lead to qualitatively different results for the size distribution and the population growth rates.     

Indirect 1H NMR characterization of H2@C60 nitroxide derivatives and their nuclear spin relaxation

(1)H NMR of two H(2)@C(60) nitroxide derivatives has been characterized indirectly by reducing to their corresponding hydroxylamines. Nuclear spin relaxation of the endohedral H(2) and external protons of the H(2)@C(60) nitroxide and its corresponding hydroxylamine were measured and analyzed. The observed spectra are consistent with negligible scalar coupling between the unpaired electron and the endo-H(2). An unexpectedly large bimolecular relaxivity induced in the hydroxylamine by the corresponding nitroxide can be explained by rapid hydrogen atom transfer between the two species.     

Saturation spectroscopy of ultraviolet transitions in mercury with a frequency-doubled cw ring dye laser

Doppler-free saturated absorption spectroscopy has been used to study the ultraviolet HgI transitions 6³P₀-6³D₁ at 296.73 nm and 6³P₀-6¹D₂ at 296.76 nm. The required tunable ultraviolet radiation was produced by a ring cavity cw dye laser with intracavity ADA frequency doubler. The isotope shifts of the 6³P⁰ -6³D₁ line for naturally abundant mercury have been measured to within a few MHz.     

Almost sure multifractal spectrum for the tip of an SLE curve

The tip multifractal spectrum of a 2-dimensional curve is one way to describe the behavior of the uniformizing conformal map of the complement near the tip. We give the tip multifractal spectrum for a Schramm?CLoewner evolution (SLE) curve, we prove that the spectrum is valid with probability 1, and we give applications to the scaling of harmonic measure at the tip.