Long-range epidemic spreading in a random environment

Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong-disorder renormalization group method and by Monte Carlo simulations in one and two spatial dimensions. Starting from a single infected site, the average survival probability is found to decay as $P(t) \sim t^{-d/z}$ up to multiplicative logarithmic corrections. Below the epidemic threshold, a Griffiths phase emerges, where the dynamical exponent $z$ varies continuously with the control parameter and tends to $z_c=d+\sigma$ as the threshold is approached. At the threshold, the spatial extension of the infected cluster (in surviving trials) is found to grow as $R(t) \sim t^{1/z_c}$ with a multiplicative logarithmic correction, and the average number of infected sites in surviving trials is found to increase as $N_s(t) \sim (\ln t)^{\chi}$ with $\chi=2$ in one dimension.Comment: 12 pages, 6 figure

Description of two-electron atoms with correct cusp conditions

New sets of functions with arbitrary large finite cardinality are constructed for two-electron atoms. Functions from these sets exactly satisfy the Kato's cusp conditions. The new functions are special linear combinations of Hylleraas- and/or Kinoshita-type terms. Standard variational calculation, leading to matrix eigenvalue problem, can be carried out to calculate the energies of the system. There is no need for optimization with constraints to satisfy the cusp conditions. In the numerical examples the ground state energy of the He atom is considered

Evidence for a high-z ISW signal from supervoids in the distribution of eBOSS quasars

The late-time integrated Sachs-Wolfe (ISW) imprint of $R\gtrsim 100~h^{-1}{\rm Mpc}$ super-structures is sourced by evolving large-scale potentials due to a dominant dark energy component in the $\Lambda$CDM model. The aspect that makes the ISW effect distinctly interesting is the repeated observation of stronger-than-expected imprints from supervoids at $z\lesssim0.9$. Here we analyze the un-probed key redshift range $0.8<z<2.2$ where the ISW signal is expected to fade in $\Lambda$CDM, due to a weakening dark energy component, and eventually become consistent with zero in the matter dominated epoch. On the contrary, alternative cosmological models, proposed to explain the excess low-$z$ ISW signals, predicted a sign-change in the ISW effect at $z\approx1.5$ due to the possible growth of large-scale potentials that is absent in the standard model. To discriminate, we estimated the high-$z$ $\Lambda$CDM ISW signal using the Millennium XXL mock catalogue, and compared it to our measurements from about 800 supervoids identified in the eBOSS DR16 quasar catalogue. At $0.8<z<1.2$, we found an excess ISW signal with $A_\mathrm{ ISW}\approx3.6\pm2.1$ amplitude. The signal is then consistent with the $\Lambda$CDM expectation ($A_\mathrm{ ISW}=1$) at $1.2<z<1.5$ where the standard and alternative models predict similar amplitudes. Most interestingly, we also detected an opposite-sign ISW signal at $1.5<z<2.2$ that is in $2.7\sigma$ tension with the $\Lambda$CDM prediction. Taken at face value, these moderately significant detections of ISW anomalies suggest an alternative growth rate of structure in low-density environments at $\sim100~h^{-1}{\rm Mpc}$ scales.Comment: 12 pages, 9 figures, submitted to MNRA

HAT-P-55b: A Hot Jupiter Transiting a Sun-like Star

We report the discovery of a new transiting extrasolar planet, HAT-P-55b. The planet orbits a V = 13.207 +/- 0.039 sun-like star with a mass of 1.013 +/- 0.037 solar masses, a radius of 1.011 +/- 0.036 solar radii and a metallicity of -0.03 +/- 0.08. The planet itself is a typical hot Jupiter with a period of 3.5852467 +/- 0.0000064 days, a mass of 0.582 +/- 0.056 Jupiter masses and a radius of 1.182 +/- 0.055 Jupiter radii. This discovery adds to the increasing sample of transiting planets with measured bulk densities, which is needed to put constraints on models of planetary structure and formation theories.Comment: 7 pages, 4 figures, accepted for publication in PAS