Signal coverage approach to the detection probability of hypothetical extraterrestrial emitters in the Milky Way

The lack of evidence for the existence of extraterrestrial life, even the simplest forms of animal life, makes it is difficult to decide whether the search for extraterrestrial intelligence (SETI) is more a high-risk, high-payoff endeavor than a futile attempt. Here we insist that even if extraterrestrial civilizations do exist and communicate, the likelihood of detecting their signals crucially depends on whether the Earth lies within a region of the galaxy covered by such signals. By considering possible populations of independent emitters in the galaxy, we build a statistical model of the domain covered by hypothetical extraterrestrial signals to derive the detection probability that the Earth is within such a domain. We show that for general distributions of the signal longevity and directionality, the mean number of detectable emitters is less than one even for detection probabilities as large as 50\%, regardless of the number of emitters in the galaxy.Comment: 9 pages, 5 figure

Continuum percolation of polydisperse hyperspheres in infinite dimensions

We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers and edges are formed between any two overlapping spheres. Edge weights naturally arise from the different radii of two overlapping spheres. For the case in which the spheres have bounded size distributions, we show that clusters of connected spheres are tree-like for $d\rightarrow \infty$ and they contain no closed loops. In this case, we find that the mean cluster size diverges at the percolation threshold density $\eta_c\rightarrow 2^{-d}$, independently of the particular size distribution. We also show that the mean number of overlaps for a particle at criticality $z_c$ is smaller than unity, while $z_c\rightarrow 1$ only for spheres with fixed radii. We explain these features by showing that in the large dimensionality limit the critical connectivity is dominated by the spheres with the largest size. Assuming that closed loops can be neglected also for unbounded radii distributions, we find that the asymptotic critical threshold for systems of spheres with radii following a lognormal distribution is no longer universal, and that it can be smaller than $2^{-d}$ for $d\rightarrow\infty$.Comment: 11 pages, 5 figure

Anisotropy of transport in bulk Rashba metals

The recent experimental discovery of three-dimensional (3D) materials hosting a strong Rashba spin-orbit coupling calls for the theoretical investigation of their transport properties. Here we study the zero temperature dc conductivity of a 3D Rashba metal in the presence of static diluted impurities. We show that, at variance with the two-dimensional case, in 3D systems spin-orbit coupling affects dc charge transport in all density regimes. We find in particular that the effect of spin-orbit interaction strongly depends on the direction of the current, and we show that this yields strongly anisotropic transport characteristics. In the dominant spin-orbit coupling regime where only the lowest band is occupied, the SO-induced conductivity anisotropy is governed entirely by the anomalous component of the renormalized current. We propose that measurements of the conductivity anisotropy in bulk Rashba metals may give a direct experimental assessment of the spin-orbit strength.Comment: 7 pages, 3 figure

Role of the particle size polydispersity in the electrical conductivity of carbon nanotube-epoxy composites

Carbon nanotubes (CTNs) with large aspect-ratios are extensively used to establish electrical connectedness in polymer melts at very low CNT loadings. However, the CNT size polydispersity and the quality of the dispersion are still not fully understood factors that can substantially alter the desired characteristics of CNT nanocomposites. Here we demonstrate that the electrical conductivity of polydisperse CNT-epoxy composites with purposely-tailored distributions of the nanotube length L is a quasiuniversal function of the first moment of L. This finding challenges the current understanding that the conductivity depends upon higher moments of the CNT length. We explain the observed quasiuniversality by a combined effect between the particle size polydispersity and clustering. This mechanism can be exploited to achieve controlled tuning of the electrical transport in general CNT nanocomposites.Comment: 9 pages, 5 figure

Unconventional dc transport in Rashba electron gases

We discuss the transport properties of a disordered two-dimensional electron gas with strong Rashba spin-orbit coupling. We show that in the high-density regime where the Fermi energy overcomes the energy associated with spin-orbit coupling, dc transport is accurately described by a standard Drude's law, due to a non-trivial compensation between the suppression of back-scattering and the relativistic correction to the quasi-particle velocity. On the contrary, when the system enters the opposite dominant spin-orbit regime, Drude's paradigm breaks down and the dc conductivity becomes strongly sensitive to the spin-orbit coupling strength, providing a suitable tool to test the entanglement between spin and charge degrees of freedom in theseComment: 6 pages, 4 figures+Supplemental Material. To appear in Phys. Rev. Let

Quantifying the information impact of future searches for exoplanetary biosignatures

One of the major goals for astronomy in the next decades is the remote search for biosignatures (i.e.\ the spectroscopic evidence of biological activity) in exoplanets. Here, we adopt a Bayesian statistical framework to discuss the implications of such future searches, both in the case when life is detected, and when no definite evidence is found. We show that even a single detection of biosignatures in the vicinity of our stellar system, in a survey of similar size to what will be obtainable in the next two decades, would affect significantly our prior belief on the frequency of life in the universe, even starting from a neutral or pessimistic stance. In particular, after such discovery, an initially agnostic observer would be led to conclude that there are more than $10^5$ inhabited planets in the galaxy with a probability exceeding $95$\%. However, this conclusion would be somewhat weakened by the viability of transfer of biological material over interstellar distances, as in panspermia scenarios. Conversely, the lack of significant evidence of biosignatures would have little effect, leaving the assessment of the abundance of life in the galaxy still largely undetermined.Comment: Published on PNA

Electrical conductivity of multi-walled carbon nanotubes-SU8 epoxy composites

We have characterized the electrical conductivity of the composite which consists of multi-walled carbon nanotubes dispersed in SU8 epoxy resin. Depending on the processing conditions of the epoxy (ranging from non-polymerized to cross-linked) we obtained tunneling and percolating-like regimes of the electrical conductivity of the composites. We interpret the observed qualitative change of the conductivity behavior in terms of reduced separation between the nanotubes induced by polymerization of the epoxy matrix.Comment: 4 pages, 3 figure