Load distribution in weighted complex networks

We study the load distribution in weighted networks by measuring the effective number of optimal paths passing through a given vertex. The optimal path, along which the total cost is minimum, crucially depend on the cost distribution function $p_c(c)$. In the strong disorder limit, where $p_c(c)\sim c^{-1}$, the load distribution follows a power law both in the Erd\H{o}s-R\'enyi (ER) random graphs and in the scale-free (SF) networks, and its characteristics are determined by the structure of the minimum spanning tree. The distribution of loads at vertices with a given vertex degree also follows the SF nature similar to the whole load distribution, implying that the global transport property is not correlated to the local structural information. Finally, we measure the effect of disorder by the correlation coefficient between vertex degree and load, finding that it is larger for ER networks than for SF networks.Comment: 4 pages, 4 figures, final version published in PR

Non-linear corrections to inflationary power spectrum

We study non-linear contributions to the power spectrum of the curvature perturbation on super-horizon scales, produced during slow-roll inflation driven by a canonical single scalar field. We find that on large scales the linear power spectrum completely dominates and leading non-linear corrections remain totally negligible, indicating that we can safely rely on linear perturbation theory to study inflationary power spectrum. We also briefly comment on the infrared and ultraviolet behaviour of the non-linear corrections.Comment: (v1) 14 pages, 2 figures; (v2) references added and discussions expanded, including a new version of Figure 2, to appear in Journal of Cosmology and Astroparticle Physic

Conserved cosmological structures in the one-loop superstring effective action

A generic form of low-energy effective action of superstring theories with one-loop quantum correction is well known. Based on this action we derive the complete perturbation equations and general analytic solutions in the cosmological spacetime. Using the solutions we identify conserved quantities characterizing the perturbations: the amplitude of gravitational wave and the perturbed three-space curvature in the uniform-field gauge both in the large-scale limit, and the angular-momentum of rotational perturbation are conserved independently of changing gravity sector. Implications for calculating perturbation spectra generated in the inflation era based on the string action are presented.Comment: 5 pages, no figure, To appear in Phys. Rev.

Topological insulators in the quaternary chalcogenide compounds and ternary famatinite compounds

We present first-principles calculations to predict several three dimensional (3D) topological insulators in quaternary chalcogenide compounds which are made of I$_2$-II-IV-VI$_4$ compositions and in ternary compositions of I$_3$-V-VI$_4$ famatinite compounds. Among the large members of these two families, we give examples of naturally occurring compounds which are mainly Cu-based chalcogenides. We show that these materials are candidates of 3D topological insulators or can be tuned to obtain topological phase transition by manipulating the atomic number of the other cation and anion elements. A band inversion can occur at a single point $\Gamma$ with considerably large inversion strength, in addition to the opening of a bulk band gap throughout the Brillouin zone. We also demonstrate that both of these families are related to each other by cross-substitutions of cations in the underlying tetragonal structure and that one can suitably tune their topological properties in a desired manner.Comment: 7 pages, 4 figure

Enumeration of simple random walks and tridiagonal matrices

We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the $n$-th power of a tridiagonal matrix and the enumeration of weighted paths of $n$ steps allows an easier combinatorial enumeration of the paths. It also seems promising for the theory of tridiagonal random matrices .Comment: several ref.and comments added, misprints correcte

Minimum-Uncertainty Angular Wave Packets and Quantized Mean Values

Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized expectation values of the conjugate momentum. This implies, for example, that the mean angular momentum is quantized for any minimum-uncertainty state obtained from any uncertainty relation involving the angular-momentum operator and a conjugate coordinate. Experiments specifically seeking to create minimum-uncertainty states localized in angular coordinates therefore must produce packets with integer angular momentum.Comment: accepted for publication in Physical Review

Evidence for Kosterlitz-Thouless type orientational ordering of CF3_3Br monolayers physisorbed on graphite

Monolayers of the halomethane CF$_3$Br adsorbed on graphite have been investigated by x-ray diffraction. The layers crystallize in a commensurate triangular lattice. On cooling they approach a three-sublattice antiferroelectric pattern of the in-plane components of the dipole moments. The ordering is not consistent with a conventional phase transition, but points to Kosterlitz-Thouless behavior. It is argued that the transition is described by a 6-state clock model on a triangular lattice with antiferromagnetic nearest neighbor interactions which is studied with Monte-Carlo simulations. A finite-size scaling analysis shows that the ordering transition is indeed in the KT universality class.Comment: 4 pages, 5 figure

Josephson Plasma in RuSr2GdCu2O8

Josephson plasma in RuSr$_{2}$GdCu$_{2}$O$_{8}$, Ru$_{1-x}$Sr$_{2}$GdCu$_{2+x}$O$_{8}$ (x = 0.3), and RuSr$_{2}$Eu$_{2-x}$Ce$_{x}$Cu$_{2}$O$_{10}$ (x = 0.5) compounds is investigated by the sphere resonance method. The Josephson plasma is observed in a low-frequency region (around 8.5 cm$^{-1}$ at T $\ll$ $T_{c}$) for ferromagnetic RuSr$_{2}$GdCu$_{2}$O$_{8}$, while it increases to 35 cm$^{-1}$ for non-ferromagnetic Ru$_{1-x}$Sr$_{2}$GdCu$_{2+x}$O$_{8}$ (x = 0.3), which represents a large reduction in the Josephson coupling at ferromagnetic RuO$_{2}$ block layers. The temperature dependence of the plasma does not shift to zero frequency ({\it i.e.} $j_{c}$ = 0) at low temperatures, indicating that there is no transition from the 0-phase to the $\pi$-phase in these compounds. The temperature dependence and the oscillator strength of the peak are different from those of other non-magnetic cuprates, and the origins of these anomalies are discussed.Comment: to appear in Phys. Rev.B Rapid Com

Dynamic behavior of driven interfaces in models with two absorbing states

We study the dynamics of an interface (active domain) between different absorbing regions in models with two absorbing states in one dimension; probabilistic cellular automata models and interacting monomer-dimer models. These models exhibit a continuous transition from an active phase into an absorbing phase, which belongs to the directed Ising (DI) universality class. In the active phase, the interface spreads ballistically into the absorbing regions and the interface width diverges linearly in time. Approaching the critical point, the spreading velocity of the interface vanishes algebraically with a DI critical exponent. Introducing a symmetry-breaking field $h$ that prefers one absorbing state over the other drives the interface to move asymmetrically toward the unpreferred absorbing region. In Monte Carlo simulations, we find that the spreading velocity of this driven interface shows a discontinuous jump at criticality. We explain that this unusual behavior is due to a finite relaxation time in the absorbing phase. The crossover behavior from the symmetric case (DI class) to the asymmetric case (directed percolation class) is also studied. We find the scaling dimension of the symmetry-breaking field $y_h = 1.21(5)$.Comment: 5 pages, 5 figures, Revte

Evidence of metallic clustering in annealed Ga1-xMnxAs from atypical scaling behavior of the anomalous Hall coefficient

We report on the anomalous Hall coefficient and longitudinal resistivity scaling relationships on a series of annealed Ga1-xMnxAs epilayers (x~0.055). As-grown samples exhibit scaling parameter n of ~ 1. Near the optimal annealing temperature, we find n ~ 2 to be consistent with recent theories on the intrinsic origins of anomalous Hall Effect in Ga1-xMnxAs. For annealing temperatures far above the optimum, we note n > 3, similar behavior to certain inhomogeneous systems. This observation of atypical behavior agrees well with characteristic features attributable to spherical resonance from metallic inclusions from optical spectroscopy measurements.Comment: 3 pages, 3 figure