Universality in Glassy Low-Temperature Physics

We propose a microscopic translationally invariant glass model which exhibits two level tunneling systems with a broad range of asymmetries and barrier heights in its glassy phase. Their distribution is qualitatively different from what is commonly assumed in phenomenological models, in that symmetric tunneling systems are systematically suppressed. Still, the model exhibits the usual glassy low-temperature anomalies. Universality is due to the collective origin of the glassy potential energy landscape. We obtain a simple explanation also for the mysterious {\em quantitative} universality expressed in the unusually narrow universal glassy range of values for the internal friction plateau.Comment: 4 pages, 5 figures, uses RevTeX

Upsilon Decay to a Pair of Bottom Squarks

We calculate the rate for $\Upsilon$ decay into a pair of bottom squarks as a function of the masses of the bottom squark and the gluino. Data from decays of the $\Upsilon$ states could provide significant new bounds on the existence and masses of these supersymmetric particles.Comment: 10 pages, latex, 2 figure

Analytical results for the distribution of shortest path lengths in random networks

We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-R\'enyi networks, based on recursion equations for the shells around a reference node and for the paths originating from it. The results are in agreement with numerical simulations for a broad range of network sizes and connectivities. The average and standard deviation of the distribution are also obtained. In the case that the mean degree scales as $N^{\alpha}$ with the network size, the distribution becomes extremely narrow in the asymptotic limit, namely almost all pairs of nodes are equidistant, at distance $d=\lfloor 1/\alpha \rfloor$ from each other. The distribution of shortest path lengths between nodes of degree $m$ and the rest of the network is calculated. Its average is shown to be a monotonically decreasing function of $m$, providing an interesting relation between a local property and a global property of the network. The methodology presented here can be applied to more general classes of networks.Comment: 12 pages, 4 figures, accepted to EP