Neutral fermion excitations in the Moore-Read state at filling factor ν = 5/2

We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux N(?)=2N-3 can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence. In the presence of two quasiparticles the same neutral fermion excitation is shown to be gapless, confirming expectations for non-abelian statistics of the Ising model with degenerate fusion channels 1 and ψ.     

Self-assembly of an optically active conjugated oligoelectrolyte

Conjugated oligoelectrolytes are of emerging technological interest due to their recent function in the fabrication of optoelectronic devices, application in biosensors, and as species that facilitate transmembrane charge migration. Solubility in aqueous, or highly polar, solvents is important for many of these applications; however, there are few studies on how the self-assembly of conjugated oligoelectrolytes into multichromophore species influences linear and nonlinear optical properties. Here, we examine 1,4-bis(4'-(N,N-bis(6'-(N,N,N-trimethylammonium)hexyl)amino)-styryl)benzene tetraiodide (DSBNI) in water, a conjugated oligoelectrolyte based on the distyrylbenzene framework. We find that DSBNI aggregation leads to increased fluorescence lifetimes, coupled with hypsochromic shifts, and larger two-photon absorption cross sections. Liquid atomic force microscopy (AFM) and cryogenic transmission electron microscopy (cryo-TEM) were used to image DSBNI aggregates and to confirm that the planar molecules stack to form nanocylinders above a critical aggregation concentration. Finally, small-angle neutron scattering (SANS) was used to quantify the aggregate dimensions in situ. Comparison of the results highlights that the hydrophilic mica surface used to image via liquid AFM and the high concentrations required for cryo-TEM facilitate the propagation of the cylinders into long fibers. SANS experiments are consistent with equivalent molecular packing geometry but lower aspect ratios. It is therefore possible to understand the evolution of optical properties as a function of concentration and aggregation and the general geometric features of the resulting supramolecular structures.     

Spectroscopic Studies of Intramolecular Proton Transfer in 2-(4-Fluorophenylamino)-5-(2,4-Dihydroxybenzeno)-1,3,4-Thiadiazole

Spectroscopic studies of the biologically active compound 2-(4-fluorophenylamino)-5-(2,4-dihydroxybenzeno)-1,3,4-thiadiazole (FABT), have been performed. Absorption studies in the UV-Vis region for FABT in polar solvents, like water or ethanol, exhibit the domination of the enol form over its keto counterpart, with a broad absorption band centered around 340 nm. In non-polar solvents such as n-heptane or heavier alkanes the 340 nm absorption band disappears and an increase of the band related to the keto form (approximately 270 nm) is observed. Fluorescence spectra (with 270 nm and 340 nm excitation energies used) show a similar dependence: for FABT in 2-propanol a peak at about 400 nm dominates over that at 330 nm while in n-heptane this relation is reversed. The solvent dependent equilibrium between the keto and enol forms is further confirmed by FTIR and Raman spectroscopies. As can be expected, this equilibrium also shows some temperature dependences. We note that the changes between the two tautomeric forms of FABT are not related to the permanent dipole moment of the solvent but rather to its dipole polarizability.     

Coloring Intersection Graphs of Arc-Connected Sets in the Plane

A family of sets in the plane is simple if the intersection of any subfamily is arc-connected, and it is pierced by a line \(L\) if the intersection of any member with \(L\) is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.     

Hydrogen-Bonded Cyclic Dimers at Large Compression: The Case of 1H-pyrrolo[3,2-h]quinoline and 2-(2′-pyridyl)pyrrole

1H-pyrrolo[3,2-h]qinoline (PQ) and 2-(2′-pyridyl)pyrrole (PP) are important systems in the study of proton-transfer reactions. These molecules possess hydrogen bond donor (pyrrole) and acceptor (pyridine) groups, which leads to the formation of cyclic dimers in their crystals. Herein, we present a joint experimental (Raman scattering) and computational (DFT modelling) study on the high-pressure behaviour of PQ and PP molecular crystals. Our results indicate that compression up to 10 GPa (100 kbar) leads to considerable strengthening of the intermolecular hydrogen bond within the cyclic dimers. However, the intramolecular N–H∙∙∙N interaction is either weakly affected by pressure, as witnessed in PQ, or weakened due to compression-induced distortions of the molecule, as was found for PP. Therefore, we propose that the compression of these systems should facilitate double proton transfer within the cyclic dimers of PQ and PP, while intramolecular transfer should either remain unaffected (for PQ) or weakened (for PP).     

On the Łojasiewicz numbers

Let f be a holomorphic function of two complex variables with an isolated critical point at $\text{0∈}\text{C}{}^2$. We give some necessary conditions for a rational number to be the smallest θ>0 in the ?ojasiewicz inequality |gradf(z)|?C|z|^θ for z near $\text{0∈}\text{C}{}^2$. To cite this article: E. Garc??a Barroso, A. P?oski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Interacting electrons on a two-dimensional surface: planar vs. spherical geometries

The center-of-mass excitations are identified in the spectrum of electrons on a two-dimensional surface in the lowest Landau level. The correspondence between the quantum numbers labeling electron states on a sphere and on a plane is drawn. The excitation spectrum on a sphere with increasing radius is shown to converge to that on a plane. In particular, in the presence of a lateral confinement (i.e. for the case of quantum dots), identical series of magic states appear in both cases. Also, a class of interaction potentials which lead to the fractional quantum Hall effect in an extended system are identified.     

Carbon and secondary deuterium kinetic isotope effects on SN2 methyl transfer reactions

Carbon and secondary deuterium kinetic isotope effect (KIE) for three types of S_N2 methyl transfer reactions have been predicted theoretically at a DFT level in gas phase and in aqueous solution modelled by the PCM continuum solvent model. No correlation between these isotope effects and geometrical features of the corresponding transition states (TSs), force constants of the imaginary frequency or Gibbs free energies of the studied reactions has been found. These findings suggest that comparative analysis of the magnitudes of the studied KIEs should be constrained to interpretation of the TS localization on the reaction coordinate only in a series of very closely related reactions. Copyright © 2007 John Wiley & Sons, Ltd.     

Stereoselective Synthesis of [Rp]-Dinucleoside (3′,5′)-Methanephosphonates

Abstract

DBU-assisted phosphonylating properties of diastereomerically pure 5′-O-DMT- thymidine (O-2,4,6-trimetylbenzoyl methanephosphonothiate)(1) towards alcohols [1] have been used for the synthesis of [Rp]-dithymidylyl(3′,5′)-methanephosphonothiótes (2) and metanephosphonates (3). Substrates (4) and (5) have been obtained according to the previously described methods [2].