Is Quantum Einstein Gravity Nonperturbatively Renormalizable?

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.Comment: 18 pages, latex, 3 figure

Yard-Sale exchange on networks: Wealth sharing and wealth appropriation

Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its properties with those in mean field (MF). Equilibrium properties in the stable phase are almost unaffected by the introduction of a network. Measurement of decorrelation times in the stable phase allow us to determine the critical interface with very good precision, and it turns out to be the same, for all networks analyzed, as the one that can be analytically derived in MF. In the unstable phase, on the other hand, dynamical as well as asymptotic properties are strongly network-dependent. Wealth no longer condenses on a single agent, as in MF, but onto an extensive set of agents, the properties of which depend on the network. Connections with previous studies of coalescence of immobile reactants are discussed, and their analytic predictions are successfully compared with our numerical results.Comment: 10 pages, 7 figures. Submitted to JSTA

Observation of Fermi-surface-dependent nodeless superconducting gaps in Ba0.6K0.4Fe2As2

The recent discovery of superconductivity in iron-arsenic compounds below a transition temperature (Tc) as high as 55K ended the monopoly of copper oxides (cuprates) in the family of high-Tc superconductors. A critical issue in understanding this new superconductor, as in the case of cuprates, is the nature, in particular the symmetry and orbital dependence, of the superconducting gap. There are conflicting experimental results, mostly from indirect measurements of the low energy excitation gap, ranging from one gap to two gaps, from line nodes to nodeless gap function in momentum space. Here we report a direct observation of the superconducting gap, including its momentum, temperature, and Fermi surface (FS) dependence in Ba0.6K0.4Fe2As2 (Tc = 37 K) using angle-resolved photoelectron spectroscopy. We find two superconducting gaps with different values: a large gap (~ 12 meV) on the two small hole-like and electron-like FS sheets, and a small gap (~ 6 meV) on the large hole-like FS. Both gaps, closing simultaneously at the bulk Tc, are nodeless and nearly isotropic around their respective FS sheets. The isotropic pairing interactions are strongly orbital dependent, as the ratio 2Delta/kBTc switches from weak to strong coupling on different bands. The same and surprisingly large superconducting gap due to strong pairing on the two small FS, which are connected by the (pi, 0) spin-density-wave vector in the parent compound, strongly suggests that the pairing mechanism originates from the inter-band interactions between these two nested FS sheets.Comment: 4 figure

Superconducting gap symmetry of Ba0.6K0.4Fe2As2 studied by angle-resolved photoemission spectroscopy

We have performed high-resolution angle-resolved photoemission spectroscopy on the optimally-doped Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ compound and determined the accurate momentum dependence of the superconducting (SC) gap in four Fermi-surface sheets including a newly discovered outer electron pocket at the M point. The SC gap on this pocket is nearly isotropic and its magnitude is comparable ($\Delta$ $\sim$ 11 meV) to that of the inner electron and hole pockets ($\sim$12 meV), although it is substantially larger than that of the outer hole pocket ($\sim$6 meV). The Fermi-surface dependence of the SC gap value is basically consistent with $\Delta$($k$) = $\Delta$$_0$cos$k_x$cos$k_y$ formula expected for the extended s-wave symmetry. The observed finite deviation from the simple formula suggests the importance of multi-orbital effects.Comment: 4 pages, 3 figures, 1 tabl

Shadow bands in single-layered Bi_2Sr_2CuO_6 studied by angle-resolved photoemission spectroscopy

We have performed systematic angle-resolved photoemission spectroscopy (ARPES) on single-layered cuprate superconductor Bi2Sr2CuO6 to elucidate the origin of shadow band. We found that the shadow band is exactly the c(2x2) replica of the main band irrespective of the carrier concentration and its intensity is invariable with respect to temperature, doping, and substitution constituents of block layers. This result rules out the possibility of antiferromagnetic correlation and supports the structural origin of shadow band. ARPES experiments on optimally doped La1.85Sr0.15CuO4 also clarified the existence of the c(2x2) shadow band, demonstrating that the shadow band is not a unique feature of Bi-based cuprates. We conclude that the shadow band is related to the orthorhombic distortion at the crystal surface.Comment: 6 pages, 4figure

Breakdown of the mean-field approximation in a wealth distribution model

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.Comment: 11 pages, 3 figure

Correlation Structures of Correlated Binomial Models and Implied Default Distribution

We show how to analyze and interpret the correlation structures, the conditional expectation values and correlation coefficients of exchangeable Bernoulli random variables. We study implied default distributions for the iTraxx-CJ tranches and some popular probabilistic models, including the Gaussian copula model, Beta binomial distribution model and long-range Ising model. We interpret the differences in their profiles in terms of the correlation structures. The implied default distribution has singular correlation structures, reflecting the credit market implications. We point out two possible origins of the singular behavior.Comment: 16 pages, 7 figure

Small-scale anisotropy of cosmic rays above 10^19eV observed with the Akeno Giant Air Shower Array

With the Akeno Giant Air Shower Array (AGASA), 581 cosmic rays above 10^19eV, 47 above 4 x 10^19eV, and 7 above 10^20eV are observed until August 1998. Arrival direction distribution of these extremely high energy cosmic rays has been studied. While no significant large-scale anisotropy is found on the celestial sphere, some interesting clusters of cosmic rays are observed. Above 4 x 10^19eV, there are one triplet and three doublets within separation angle of 2.5^o and the probability of observing these clusters by a chance coincidence under an isotropic distribution is smaller than 1 %. Especially the triplet is observed against expected 0.05 events. The cos(\theta_GC) distribution expected from the Dark Matter Halo model fits the data as well as an isotropic distribution above 2 x 10^19eV and 4 x 10^19eV, but is a poorer fit than isotropy above 10^19eV. Arrival direction distribution of seven 10^20eV cosmic rays is consistent with that of lower energy cosmic rays and is uniform. Three of seven are members of doublets above about 4 x 10^19eV.Comment: 40 pages, 12 figure, AASTeX *** Authors found a typo on Table 2 -- Energy of event 94/07/06 **

Infectious Default Model with Recovery and Continuous Limit

We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are described by Y_{ij} and Y'_{ij}. We obtain the default probability function P(k) for k defaults. Taking its continuous limit, we find two nontrivial probability distributions with the reflection symmetry of S_{i} \leftrightarrow 1-S_{i}. Their profiles are singular and oscillating and we understand it theoretically. We also compare P(k) with an implied default distribution function inferred from the quotes of iTraxx-CJ. In order to explain the behavior of the implied distribution, the recovery effect may be necessary.Comment: 13 pages, 7 figure