Entropy measures for complex networks: Toward an information theory of complex topologies

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.Comment: (4 pages, 1 figure

Astrometry and Photometry with Coronagraphs

We propose a solution to the problem of astrometric and photometric calibration of coronagraphic images with a simple optical device which, in theory, is easy to use. Our design uses the Fraunhofer approximation of Fourier optics. Placing a periodic grid of wires (we use a square grid) with known width and spacing in a pupil plane in front of the occulting coronagraphic focal plane mask produces fiducial images of the obscured star at known locations relative to the star. We also derive the intensity of these fiducial images in the coronagraphic image. These calibrator images can be used for precise relative astrometry, to establish companionship of other objects in the field of view through measurement of common proper motion or common parallax, to determine orbits, and to observe disk structure around the star quantitatively. The calibrator spots also have known brightness, selectable by the coronagraph designer, permitting accurate relative photometry in the coronagraphic image. This technique, which enables precision exoplanetary science, is relevant to future coronagraphic instruments, and is particularly useful for `extreme' adaptive optics and space-based coronagraphy.Comment: To appear in ApJ August 2006, 27 preprint style pages 4 figure

Physical Properties of Metallic Antiferromagnetic CaCo{1.86}As2 Single Crystals

We report studies of CaCo{1.86}As2 single crystals. The electronic structure is probed by angle-resolved photoemission spectroscopy (ARPES) measurements of CaCo{1.86}As2 and by full-potential linearized augmented-plane-wave calculations for the supercell Ca8Co15As16 (CaCo{1.88}As2). Our XRD crystal structure refinement is consistent with the previous combined refinement of x-ray and neutron powder diffraction data showing a collapsed-tetragonal ThCr2Si2-type structure with 7(1)% vacancies on the Co sites corresponding to the composition CaCo{1.86}As2 [D. G. Quirinale et al., Phys. Rev. B 88, 174420 (2013)]. The anisotropic magnetic susceptibility chi(T) data are consistent with the magnetic neutron diffraction data of Quirianale et al. that demonstrate the presence of A-type collinear antiferromagnetic order below the Neel temperature TN = 52(1) K with the easy axis being the tetragonal c axis. However, no clear evidence from the resistivity rho(T) and heat capacity Cp(T) data for a magnetic transition at TN is observed. A metallic ground state is demonstrated from band calculations and the rho(T), Cp(T) and ARPES data, and spin-polarized calculations indicate a competition between the A-type AFM and FM ground states. The Cp(T) data exhibit a large Sommerfield electronic coefficient reflecting a large density of states at the Fermi energy D(EF), consistent with the band structure calculations which also indicate a large D(EF) arising from Co 3d bands. At 1.8 K the M(H) data for H|| c exhibit a well-defined first-order spin-flop transition at an applied field of 3.5 T. The small ordered moment of 0.3 muB/Co obtained from the M(H) data at low T, the large exchange enhancement of chi and the lack of a self-consistent interpretation of the chi(T) and M(H,T) data in terms of a local moment Heisenberg model together indicate that the magnetism of CaCo{1.86}As2 is itinerant.Comment: 18 pages, 15 figures, 4 tables, 61 references; v2: extended the fits of experimental data by additional electronic structure calculations; published versio

Ferromagnetic Ordering in CeIr2B2: Transport, magnetization, specific heat and NMR studies

We present a complete characterization of ferromagnetic system CeIr2B2 using powder x-ray diffraction XRD, magnetic susceptibility chi(T), isothermal magnetization M(H), specific heat C(T), electrical resistivity rho(T,H), and thermoelectric power S(T) measurements. Furthermore 11B NMR study was performed to probe the magnetism on a microscopic scale. The chi(T), C(T) and rho(T) data confirm bulk ferromagnetic ordering with Tc = 5.1 K. Ce ions in CeIr2B2 are in stable trivalent state. Our low-temperature C(T) data measured down to 0.4 K yield Sommerfeld coefficient gamma = 73(4) mJ/molK2 which is much smaller than the previously reported value of gamma = 180 mJ/molK2 deduced from the specific heat measurement down to 2.5 K. For LaIr2B2 gamma = 6(1) mJ/molK2 which implies the density of states at the Fermi level D(EF) = 2.54 states/(eV f.u.) for both spin directions. The renormalization factor for quasi-particle density of states and hence for quasi-particle mass due to 4f correlations in CeIr2B2 is 12. The Kondo temperature TK ~ 4 K is estimated from the jump in specific heat of CeIr2B2 at Tc. Both C(T) and rho(T) data exhibit gapped-magnon behavior in magnetically ordered state with an energy gap Eg ~ 3.5 K. The rho data as a function of magnetic field H indicate a large negative magnetoresistance (MR) which is highest for T = 5 K.While at 5 K the negative MR keeps on increasing up to 10 T, at 2 K an upturn is observed near H = 3.5 T. On the other hand, the thermoelectric power data have small absolute values (S ~ 7 {\mu}V/K) indicating a weak Kondo interaction. A shoulder in S(T) at about 30 K followed by a minimum at ~ 10 K is attributed to crystal electric field (CEF) effects and the onset of magnetic ordering. 11B NMR line broadening provides strong evidence of ferromagnetic correlations below 40 K.Comment: 10 pages, 11 figure

Investigation of the magnetic structure and crystal field states of pyrochlore antiferromagnet Nd2Zr2O7

We present synchrotron x-ray diffraction, neutron powder diffraction and time-of-flight inelastic neutron scattering measurements on the rare earth pyrochlore oxide Nd2Zr2O7 to study the ordered state magnetic structure and cystal field states. The structural characterization by high-resolution synchrotron x-ray diffraction confirms that the pyrochlore structure has no detectable O vacancies or Nd/Zr site mixing. The neutron diffraction reveals long range all-in/all-out antiferromagnetic order below T_N ~ 0.4 K with propagation vector k = (0 0 0) and an ordered moment of 1.26(2) \mu_B/Nd at 0.1 K. The ordered moment is much smaller than the estimated moment of 2.65 \mu_B/Nd for the local Ising ground state of Nd3+ (J=9/2) suggesting that the ordering is partially suppressed by quantum fluctuations. The strong Ising anisotropy is further confirmed by the inelastic neutron scattering data which reveals a well-isolated dipolar-octupolar type Kramers doublet ground state. The crystal field level scheme and ground state wavefunction have been determined.Comment: 12 pages, 15 figures, 2 table

Effective One-Dimensional Coupling in the Highly-Frustrated Square-Lattice Itinerant Magnet CaCo2−y_{\mathrm{2}-y}As2_{2}

Inelastic neutron scattering measurements on the itinerant antiferromagnet (AFM) CaCo$_{\mathrm{2}-y}$As$_{2}$ at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. These results are shown to arise from near-perfect bond frustration within the $J_1$-$J_2$ Heisenberg model on a square lattice with ferromagnetic $J_1$, and hence indicate that the extensive previous experimental and theoretical study of the $J_1$-$J_2$ Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems

Ba{1-x}KxMn2As2: An Antiferromagnetic Local-Moment Metal

The compound BaMn2As2 with the tetragonal ThCr2Si2 structure is a local-moment antiferromagnetic insulator with a Neel temperature TN = 625 K and a large ordered moment mu = 3.9 mu_B/Mn. We demonstrate that this compound can be driven metallic by partial substitution of Ba by K, while retaining the same crystal and antiferromagnetic structures together with nearly the same high TN and large mu. Ba_{1-x}K_xMn2As2 is thus the first metallic ThCr2Si2-type MAs-based system containing local 3d transition metal M magnetic moments, with consequences for the ongoing debate about the local moment versus itinerant pictures of the FeAs-based superconductors and parent compounds. The Ba_{1-x}K_xMn2As2 class of compounds also forms a bridge between the layered iron pnictides and cuprates and may be useful to test theories of high Tc superconductivity.Comment: 5 two-column typeset pages, 5 figures, 20 references; v2: minor revisions, 4 new references, published versio