Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, $f(t)=f_0\exp[-(t/\tau)^\beta]$, with the exponent $\beta$ increasing with the temperature. The relaxation time follows an Arrhenius behavior divergence when $T\to 0$. A relation between the specific heat and the entropy in the long time regime is found.Comment: 5 pages and 4 figure

Glory revealed in disk-integrated photometry of Venus

Context. Reflected light from a spatially unresolved planet yields unique insight into the overall optical properties of the planet cover. Glories are optical phenomena caused by light that is backscattered within spherical droplets following a narrow distribution of sizes; they are well known on Earth as localised features above liquid clouds. Aims. Here we report the first evidence for a glory in the disk-integrated photometry of Venus and, in turn, of any planet. Methods. We used previously published phase curves of the planet that were reproduced over the full range of phase angles with model predictions based on a realistic description of the Venus atmosphere. We assumed that the optical properties of the planet as a whole can be described by a uniform and stable cloud cover, an assumption that agrees well with observational evidence. Results. We specifically show that the measured phase curves mimic the scattering properties of the Venus upper-cloud micron-sized aerosols, also at the small phase angles at which the glory occurs, and that the glory contrast is consistent with what is expected after multiple scattering of photons. In the optical, the planet appears to be brighter at phase angles of 11-13 deg than at full illumination; it undergoes a maximum dimming of up to 10 percent at phases in between. Conclusions. Glories might potentially indicate spherical droplets and, thus, extant liquid clouds in the atmospheres of exoplanets. A prospective detection will require exquisite photometry at the small planet-star separations of the glory phase angles.Comment: In press. Astronomy & Astrophysics. Letter to the Editor; 201

Time Scales in Evolutionary Dynamics

Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction and selection leads to dramatic changes in the outcome of evolution. Examples include the selection of the inefficient strategy in the Harmony and Stag-Hunt games, and the disappearance of the coexistence state in the Snowdrift game. Our results hold for any population size and in the presence of a background of fitness.Comment: Final version with minor changes, accepted for publication in Physical Review Letter