Spectral distributions of adjacency and Laplacian matrices of random graphs

In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the Laplacian matrices; (ii) under some further independent conditions, the normalized largest eigenvalues of the Laplacian matrices are dense in a compact interval almost surely; (iii) the empirical distributions of the eigenvalues of the Laplacian matrices converge weakly to the free convolution of the standard Gaussian distribution and the Wigner's semi-circular law; (iv) the empirical distributions of the eigenvalues of the adjacency matrices converge weakly to the Wigner's semi-circular law.Comment: Published in at http://dx.doi.org/10.1214/10-AAP677 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Comment on " a unified scheme for flavored mesons and baryons"

We would comment on the results of the paper "a unified scheme for flavored mesons and baryons" (P.C.Vinodkumar, J.N.Panandya, V.M.Bannur, and S.B.Khadkikar Eur. Phys. J. A4(1999)83), and point out some inconsistencies and mistakes in the work for solving the Dirac equation. In terms of an example for a single particle we investigate the reliability of the perturbative method for computing the Coulomb energy and discuss the contribution to the wavefunction at origin from the Coulomb potential. We conclude that the accuracy of their numerical results needs to be reconsidered.Comment: Latex file, 11page

Two parameters scaling approach to Anderson localization of weekly interacting BEC

We numerically study the Anderson localization of weekly interacting Bose-Einstein condensate in a one-dimensional disordered potential. We show that two parameters are needed to completely describe such system, and the density profile of which can be described with the sum of two exponential functions. This is a new attempt for precise description of systems with interplay of disorder and interaction.Comment: Version accepted by JETP Letter

Molecular States and 1^-+ Exotic Mesons

This work investigates whether the observed 1^-+ exotic mesons are molecular states. We first use a potential model to calculate the spectra and lifetimes of the f_0(980) and a_0(980), taken to be loosely bound molecular states of K Kbar, then apply the same scenario to the 1^-+ exotic states pi_1(1400) and pi_1(1600), assuming them to be pi eta(1295) and pi eta(1440) molecules respectively. We derive the effective potential in the framework of field theory at the hadronic level. Our results indicate that the present data on pi_1(1400) and pi_1(1600) rule out the specific molecular ansatz. We show that the lifetime of a loosely bound heavy-light molecule with enough angular momentum is fully determined by the lifetimes of its constituent mesons.Comment: 23 pages, 1 figure, LaTe

Bright broad-band afterglows of gravitational wave bursts from mergers of binary neutron stars

If double neutron star mergers leave behind a massive magnetar rather than a black hole, a bright early afterglow can follow the gravitational wave burst (GWB) even if there is no short gamma-ray burst (SGRB) - GWB association or there is an association but the SGRB does not beam towards earth. Besides directly dissipating the proto-magnetar wind as suggested by Zhang, we here suggest that the magnetar wind could push the ejecta launched during the merger process, and under certain conditions, would reach a relativistic speed. Such a magnetar-powered ejecta, when interacting with the ambient medium, would develop a bright broad-band afterglow due to synchrotron radiation. We study this physical scenario in detail, and present the predicted X-ray, optical and radio light curves for a range of magnetar and ejecta parameters. We show that the X-ray and optical lightcurves usually peak around the magnetar spindown time scale (10^3-10^5s), reaching brightness readily detectable by wide-field X-ray and optical telescopes, and remain detectable for an extended period. The radio afterglow peaks later, but is much brighter than the case without a magnetar energy injection. Therefore, such bright broad-band afterglows, if detected and combined with GWBs in the future, would be a probe of massive millisecond magnetars and stiff equation-of-state for nuclear matter.Comment: ApJ, in pres