Crystal Structure and Magnetism of the Linear-Chain Copper Oxides Sr5Pb3-xBixCuO12

The title quasi-1D copper oxides (0=< x =<0.4) were investigated by neutron diffraction and magnetic susceptibility studies. Polyhedral CuO4 units in the compounds were found to comprise linear-chains at inter-chain distance of approximately 10 A. The parent chain compound (x = 0), however, shows less anisotropic magnetic behavior above 2 K, although it is of substantially antiferromagnetic (mu_{eff}= 1.85 mu_{B} and Theta_{W} = -46.4 K) spin-chain system. A magnetic cusp gradually appears at about 100 K in T vs chi with the Bi substitution. The cusp (x = 0.4) is fairly characterized by and therefore suggests the spin gap nature at Delta/k_{B} ~ 80 K. The chain compounds hold electrically insulating in the composition range.Comment: To be published in PR

Stability of temporal statistics in Transition Path Theory with sparse data

Transition Path Theory (TPT) provides a rigorous statistical characterization of the ensemble of trajectories connecting directly, i.e., without detours, two disconnected (sets of) states in a Markov chain, a stochastic process that undergoes transitions from one state to another with probability depending on the state attained in the previous step. Markov chains can be constructed using trajectory data via counting of transitions between cells covering the domain spanned by trajectories. With sparse trajectory data, the use of regular cells is observed to result in unstable estimates of the total duration of transition paths. Using Voronoi cells resulting from k-means clustering of the trajectory data, we obtain stable estimates of this TPT statistic, which is generalized to frame the remaining duration of transition paths, a new TPT statistic suitable for investigating connectivity.Comment: Submitted to Chaos. Comments welcomed

Resonance production from jet fragmentation

Short lived resonances are sensitive to the medium properties in heavy-ion collisions. Heavy hadrons have larger probability to be produced within the quark gluon plasma phase due to their short formation times. Therefore heavy mass resonances are more likely to be affected by the medium, and the identification of early produced resonances from jet fragmentation might be a viable option to study chirality. The high momentum resonances on the away-side of a triggered di-jet are likely to be the most modified by the partonic or early hadronic medium. We will discuss first results of triggered hadron-resonance correlations in Cu+Cu heavy ion collisions.Comment: Hot Quarks Colorado 2008 Proceedings, 4 pages 5 figure

Efficient Comparison of Massive Graphs Through The Use Of 'Graph Fingerprints'

The problem of how to compare empirical graphs is an area of great interest within the field of network science. The ability to accurately but efficiently compare graphs has a significant impact in such areas as temporal graph evolution, anomaly detection and protein comparison. The comparison problem is compounded when working with graphs containing millions of anonymous, i.e. unlabelled, vertices and edges. Comparison of two or more graphs is highly computationally expensive. Thus reducing a graph to a much smaller feature set – called a fingerprint, which accurately captures the essence of the graph would be highly desirable. Such an approach would have potential applications outside of graph comparisons, especially in the area of machine learning. This paper introduces a feature extraction based approach for the efficient comparison of large topologically similar, but order varying, unlabelled graph datasets. The approach acts by producing a ‘Graph Fingerprint’ which represents both vertex level and global level topological features from a graph. The approach is shown to be efficient when comparing graphs which are highly topologically similar but order varying. The approach scales linearly with the size and complexity of the graphs being fingerprinted

Exact diagonalization of the S=1/2 Heisenberg antiferromagnet on finite bcc lattices to estimate properties on the infinite lattice

Here we generate finite bipartite body-centred cubic lattices up to 32 vertices. We have studied the spin one half Heisenberg antiferromagnet by diagonalizing its Hamiltonian on each of the finite lattices and hence computing its ground state properties. By extrapolation of these data we obtain estimates of the T = 0 properties on the infinite bcc lattice. Our estimate of the T = 0 energy agrees to five parts in ten thousand with third order spin wave and series expansion method estimates, while our estimate of the staggered magnetization agrees with the spin wave estimate to within a quarter of one percent.Comment: 16 pages, LaTeX, 1 ps figure, to appear in J.Phys.

Magnetic Properties of (VO)_2P_2O_7 from Frustrated Interchain Coupling

Neutron-scattering experiments on (VO)_2P_2O_7 reveal both a gapped magnon dispersion and an unexpected, low-lying second mode. The proximity and intensity of these modes suggest a frustrated coupling between the alternating spin chains. We deduce the minimal model containing such a frustration, and show that it gives an excellent account of the magnon dispersion, static susceptibility and electron spin resonance absorption. We consider two-magnon states which bind due to frustration, and demonstrate that these may provide a consistent explanation for the second mode.Comment: RevTeX, 5 pages, 6 figures, compressed from first versio

Spin gap in the Quasi-One-Dimensional S=1/2 Antiferromagnet: Cu2(1,4-diazacycloheptane)2Cl4

Cu_{2}(1,4-diazacycloheptane)_{2}Cl_{4} contains double chains of spin 1/2 Cu^{2+} ions. We report ac susceptibility, specific heat, and inelastic neutron scattering measurements on this material. The magnetic susceptibility, $\chi(T)$, shows a rounded maximum at T = 8 K indicative of a low dimensional antiferromagnet with no zero field magnetic phase transition. We compare the $\chi(T)$ data to exact diagonalization results for various one dimensional spin Hamiltonians and find excellent agreement for a spin ladder with intra-rung coupling $J_1 = 1.143(3)$ meV and two mutually frustrating inter-rung interactions: $J_2 = 0.21(3)$ meV and $J_3 = 0.09(5)$ meV. The specific heat in zero field is exponentially activated with an activation energy $\Delta = 0.89(1)$ meV. A spin gap is also found through inelastic neutron scattering on powder samples which identify a band of magnetic excitations for $0.8 < \hbar\omega < 1.5$ meV. Using sum-rules we derive an expression for the dynamic spin correlation function associated with non-interacting propagating triplets in a spin ladder. The van-Hove singularities of such a model are not observed in our scattering data indicating that magnetic excitations in Cu_{2}(1,4-diazacycloheptane)_{2}Cl_{4} are more complicated. For magnetic fields above $H_{c1} \simeq 7.2$ T specific heat data versus temperature show anomalies indicating a phase transition to an ordered state below T = 1 K.Comment: 9 pages, 8 postscript figures, LaTeX, Submitted to PRB 8/4/97, e-mail Comments to [email protected]