Network Density of States

Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of associated differential operators. But the translation from spectral geometry to spectral graph theory has largely focused on results involving only a few extreme eigenvalues and their associated eigenvalues. Unlike in geometry, the study of graphs through the overall distribution of eigenvalues - the spectral density - is largely limited to simple random graph models. The interior of the spectrum of real-world graphs remains largely unexplored, difficult to compute and to interpret. In this paper, we delve into the heart of spectral densities of real-world graphs. We borrow tools developed in condensed matter physics, and add novel adaptations to handle the spectral signatures of common graph motifs. The resulting methods are highly efficient, as we illustrate by computing spectral densities for graphs with over a billion edges on a single compute node. Beyond providing visually compelling fingerprints of graphs, we show how the estimation of spectral densities facilitates the computation of many common centrality measures, and use spectral densities to estimate meaningful information about graph structure that cannot be inferred from the extremal eigenpairs alone.Comment: 10 pages, 7 figure

An ultrahigh-vacuum cryostat for simultaneous scanning tunneling microscopy and magneto-transport measurements down to 400mK

We present the design and calibration measurements of a scanning tunneling microscope setup in a 3He ultrahigh-vacuum cryostat operating at 400 mK with a hold time of 10 days. With 2.70 m in height and 4.70 m free space needed for assembly, the cryostat fits in a one-story lab building. The microscope features optical access, an xy table, in situ tip and sample exchange, and enough contacts to facilitate atomic force microscopy in tuning fork operation and simultaneous magneto-transport measurements on the sample. Hence, it enables scanning tunneling spectroscopy on microstructured samples which are tuned into preselected transport regimes. A superconducting magnet provides a perpendicular field of up to 14 T. The vertical noise of the scanning tunneling microscope amounts to 1 pmrms within a 700 Hz bandwidth. Tunneling spectroscopy using one superconducting electrode revealed an energy resolution of 120 mueV. Data on tip-sample Josephson contacts yield an even smaller feature size of 60 mueV, implying that the system operates close to the physical noise limit.Comment: 12 pages, 11 figure

Symmetry of bound and antibound states in the semiclassical limit

We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h. This simple result was inspired by a numerical experiment and we describe the numerical scheme for an efficient computation of resonances in one dimension

Centrality dependence of charged antiparticle to particle ratios near mid-rapidity in d+Au collisions at sqrt(s_NN)=200 GeV

The ratios of the yields of charged antiparticles to particles have been obtained for pions, kaons, and protons near mid-rapidity for d+Au collisions at sqrt(s_NN) = 200 GeV as a function of centrality. The reported values represent the ratio of the yields averaged over the rapidity range of 0.1<y_pi<1.3 and 0<y_(K,p)<0.8, where positive rapidity is in the deuteron direction, and for transverse momenta 0.1<p_(T)^(pi,K)<1.0 GeV/c and 0.3<p_(T)^(p)<1.0 GeV/c. Within the uncertainties, a lack of centrality dependence is observed in all three ratios. The data are compared to results from other systems and model calculations.Comment: 6 pages, 4 figures, submitted to PR

System Size, Energy and Centrality Dependence of Pseudorapidity Distributions of Charged Particles in Relativistic Heavy Ion Collisions

We present the first measurements of the pseudorapidity distribution of primary charged particles in Cu+Cu collisions as a function of collision centrality and energy, \sqrtsnn = 22.4, 62.4 and 200 GeV, over a wide range of pseudorapidity, using the PHOBOS detector. Making a global comparison of Cu+Cu and Au+Au results, we find that the total number of produced charged particles and the rough shape (height and width) of the pseudorapidity distributions are determined by the number of nucleon participants. More detailed studies reveal that a more precise matching of the shape of the Cu+Cu and Au+Au pseudorapidity distributions over the full range of pseudorapidity occurs for the same Npart/2A value rather than the same Npart value. In other words, it is the collision geometry rather than just the number of nucleon participants that drives the detailed shape of the pseudorapidity distribution and its centrality dependence at RHIC energies.Comment: Submitted to Physical Review Letter

System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow

This paper presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider (RHIC). The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system

Latest Results from PHOBOS

This manuscript contains a summary of the latest physics results from PHOBOS, as reported at Quark Matter 2006. Highlights include the first measurement from PHOBOS of dynamical elliptic flow fluctuations as well as an explanation of their possible origin, two-particle correlations, identified particle ratios, identified particle spectra and the latest results in global charged particle production.Comment: 9 pages, 7 figures, PHOBOS plenary proceedings for Quark Matter 200