Persistent supersolid phase of hard-core bosons on the triangular lattice

We study hard-core bosons with unfrustrated hopping (t) and nearest neighbor repulsion (U) (spin S=1/2 XXZ model) on the triangular lattice. At half filling, the system undergoes a zero temperature (T) quantum phase transition from a superfluid phase at small U to a supersolid at Uc approximately 4.45 in units of 2t. This supersolid phase breaks the lattice translation symmetry in a characteristic sqrt[3] x square root of 3 pattern, and is remarkably stable--indeed, a smooth extrapolation of our results indicates that the supersolid phase persists for arbitrarily large U/t.     

Anomalous <Emphasis Type="Italic">VVH</Emphasis> interactions at a linear collider

We examine, in a model independent way, the sensitivity of a linear collider to the couplings of a light Higgs boson to a pair of gauge bosons, including the possibility of CP violation. We construct several observables that probe the various possible anomalous couplings. For an intermediate mass Higgs, a collider operating at a center of mass energy of 500 GeV and with an integrated luminosity of 500 fb⁻¹ is shown to be able to constrain the ZZH vertex at the few per cent level, with even higher sensitivity for some of the couplings. However, lack of sufficient number of observables as well as contamination from the ZZH vertex limits the precision to which anomalous part of the WWH coupling can be probed.      

Graviton resonances in e<Superscript>+</Superscript>e<Superscript>-</Superscript>→μ<Superscript>+</Superscript>μ<Superscript>-</Superscript> at linear colliders with beamstrahlung and ISR effects

The electromagnetic radiation emitted by colliding beams is expected to play an important role at the next generation of high energy e⁺e^- linear colliders. Focussing on the simplest process, e⁺e^-→μ⁺μ^-, we show that, for suitable machine parameters and luminosity, radiative effects like initial state radiation (ISR) and beamstrahlung can be used to search for resonant graviton modes of the Randall–Sundrum model in an efficient manner.     

Formulae and Recursions for the Joint Distribution of Success Runs of Several Lengths

Consider a sequence of n independent Bernoulli trials with the j-th trial having probability pj of success, 1 j n. Let M(n,K) and N(n, K) denote, respectively, the r-dimensional random variables (M(n, k1),..., M(n,kr) and (N(n,k1), ..., N(n, kr)), where K = (k1, k2, ..., kr) and M(n, s) [N(n, s)] represents the number of overlapping [non-overlapping] success runs of length s. We obtain exact formulae and recursions for the probability distributions of M(n, K) and N(n, K). The techniques of proof employed include the inclusion-exclusion principle and generating function methodology. Our results have potential applications to statistical tests for randomness.     

Synthesis and characterization of novel chiral imidazolium and pyridinium ionic liquids derived from tartaric acid and 2-oxazolidinone

Abstract

Novel chiral imidazolium and pyridinium ionic liquids based on tartaric acid and 2-oxazolidinone were designed. Symmetrical dicationic ionic liquids based on tartaric acid have been synthesized and characterized. These chiral ionic liquids were designed by employing very short and simple methods. Incorporation of alkyl halide over tartaric acid and 2-oxazolidinone is an important step. N-methyl imidazole and pyridine were used for preparation of quaternary salts. These ionic liquids have been evaluated for the asymmetric sulfide oxidation. Chiral ionic liquids based on tartaric acid showed superior chiral inducing property as compare to 2-oxazolidinone based chiral ionic liquids.     

Stereochemical influence of the ligand on the structure of manganese complexes: implications for catalytic epoxidations

Manganese complexes of the ligand HphoxCOOR (R=H or Me) have been synthesized and characterized by X-ray analysis, ESI-MS, ligand-field spectroscopy, electrochemistry, and paramagnetic 1H NMR. The ligands, chirally pure or racemic, influence the structures of the complexes formed. Manganese(III) complexes of the ligand HphoxCOOMe are square-pyramidal or octahedral with two ligands bound in a trans fashion in the solid state. The racemic ligand (RS-HphoxCOOMe) as well as the enantiopure ligand (R-HphoxCOOMe) forms manganese complexes with similar solid-state structures. Ligand-exchange reactions occur in solution giving rise to meso complexes as confirmed by ESI-MS and deuteration studies. The manganese(III) complex of R-HphoxCOOH is octahedral, with two dianionic ligands bound in a fac-cct fashion in a tridentate manner. The manganese(III) complex of RS-HphoxCOOH is also octahedral with two dianionic ligands now bound in a trans fashion in a didentate manner and with two water molecules occupying axial sites. The paramagnetic 1H NMR spectra of the complexes have been interpreted on the basis of the relaxation times with the help of the inversion-recovery pulse technique. The binding of imidazole with the metal center depends on the chirality of the ligands in the metal complexes of HphoxCOOMe. Imidazole coordination was found to occur with the metal complex that contains two ligands with the same chirality (R and R) (R-1), while no imidazole coordination was found upon reaction with the metal complex that contains two ligands with opposite chirality (R and S) (RS-1). Epoxidation reactions of various alkenes with H2O2 as the oxidant reveal that the complexes give turnover numbers in the range of 10-35, the epoxide being the major product. The catalytic activity depends on the additives used, and a clear base effect is observed. The turnover numbers have been found to be higher in the complexes where no binding of N-Meim is observed. The latter fact unambiguously shows that imidazole binding is not a prerequisite for higher turnover numbers, in contrast to the Mn-Schiff base catalysts.     

Universal and Overlap Cycles for Posets,Words, and Juggling Patterns

We discuss results dealing with universal cycles (ucycles) and s-overlap cycles, and contribute to the body of those results by proving existence of universal cycles of naturally labeled posets (NL posets), s-overlap cycles of words of weight k, and juggling patterns. The result on posets is, to the best of our knowledge, the first demonstration of the existence of a ucycle whose length is unknown.     

The Number of Seymour Vertices in Random Tournaments and Digraphs

Seymour’s distance two conjecture states that in any digraph there exists a vertex (a “Seymour vertex”) that has at least as many neighbors at distance two as it does at distance one. We explore the validity of probabilistic statements along lines suggested by Seymour’s conjecture, proving that almost surely there are a “large” number of Seymour vertices in random tournaments and “even more” in general random digraphs.