We perform the first one-point fluctuation analysis of the high-energy neutrino sky. This method reveals itself to be especially suited to contemporary neutrino data, as it allows to study the properties of the astrophysical components of the high-energy flux detected by the IceCube telescope, even with low statistics and in the absence of point source detection. Besides the veto-passing atmospheric foregrounds, we adopt a simple model of the high-energy neutrino background by assuming two main extra-galactic components: star-forming galaxies and blazars. By leveraging multi-wavelength data from Herschel and Fermi, we predict the spectral and anisotropic probability distributions for their expected neutrino counts in IceCube. We find that star-forming galaxies are likely to remain a diffuse background due to the poor angular resolution of IceCube, and we determine an upper limit on the number of shower events that can reasonably be associated to blazars. We also find that upper limits on the contribution of blazars to the measured flux are unfavourably affected by the skewness of the blazar flux distribution. One-point event clustering and likelihood analyses of the IceCube HESE data suggest that this method has the potential to dramatically improve over more conventional model-based analyses, especially for the next generation of neutrino telescopes.

After the discovery of extraterrestrial high-energy neutrinos, the next major goal of neutrino telescopes will be identifying astrophysical objects that produce them. The flux of the brightest source $F_{\rm max}$, however, cannot be probed by studying the diffuse neutrino intensity. We aim at constraining $F_{\rm max}$ by adopting a broken power-law flux distribution, a hypothesis supported by observed properties of any generic astrophysical sources. The first estimate of $F_{\rm max}$ comes from the fact that we can only observe one universe, and hence, the expected number of sources above $F_{\rm max}$ cannot be too small compared with one. For abundant source classes such as starburst galaxies, this one-source constraint yields a value of $F_{\rm max}$ that is an order of magnitude lower than the current upper limits from point-source searches. Then we derive upper limits on $F_{\rm max}$ assuming that the angular power spectrum is consistent with neutrino shot noise yet. We find that the limits obtained with upgoing muon neutrinos in IceCube can already be quite competitive, especially for rare but bright source populations such as blazars. The limits will improve nearly quadratically with exposure, and therefore be even more powerful for the next generation of neutrino telescopes.Comment: 13 pages, 10 figures, accepted by Phys.Rev.

Abstract. The one-point function (i.e., the isotropic flux distribution) is a complementary method to (anisotropic) two-point correlations in searches for a gamma-ray dark matter annihilation signature. Using analytical models of structure formation and dark matter halo properties, we compute the gamma-ray flux distribution due to annihilations in extragalactic dark matter halos, as it would be observed by the Fermi Large Area Telescope. Combining the central limit theorem and Monte Carlo sampling, we show that the flux distribution takes the form of a narrow Gaussian of 'diffuse' light, with an 'unresolved point source' power-law tail as a result of bright halos. We argue that this background due to dark matter constitutes an irreducible and significant background component for point-source annihilation searches with galaxy clusters and dwarf spheroidal galaxies, modifying the predicted signal-to-noise ratio. A study of astrophysical backgrounds to this signal reveals that the shape of the total gamma-ray flux distribution is very sensitive to the contribution of a dark matter component, allowing us to forecast promising one-point upper limits on the annihilation cross section. We show that by using the flux distribution at only one energy bin, one can probe the canonical cross section required for explaining the relic density, for dark matter of masses around tens of GeV.

Weak values are average quantities, therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as possible, building primarily on material from Moyal (Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, Cambridge, 1949) and Sonego (Found Phys 21(10):1135, 1991) . The weak variance is defined in terms of the Wigner function, using a standard construction from probability theory. We show this corresponds to a measurable quantity, which is not itself a weak value. It also leads naturally to a connection between the imaginary part of the weak value of momentum and the quantum potential. We study how the negativity of the Wigner function causes negative weak variances, and the implications this has on a class of 'subquantum' theories. We also discuss the role of weak variances in studying determinism, deriving the classical limit from a variational principle.

The one-point function (i.e., the isotropic flux distribution) is a complementary method to (anisotropic) two-point correlations in searches for a gamma-ray dark matter annihilation signature. Using analytical models of structure formation and dark matter halo properties, we compute the gamma-ray flux distribution due to annihilations in extragalactic dark matter halos, as it would be observed by the Fermi Large Area Telescope. Combining the central limit theorem and Monte Carlo sampling, we show that the flux distribution takes the form of a narrow Gaussian of 'diffuse' light, with an 'unresolved point source' power-law tail as a result of bright halos. We argue that this background due to dark matter constitutes an irreducible and significant background component for point-source annihilation searches with galaxy clusters and dwarf spheroidal galaxies, modifying the predicted signal-to-noise ratio. A study of astrophysical backgrounds to this signal reveals that the shape of the total gamma-ray flux distribution is very sensitive to the contribution of a dark matter component, allowing us to forecast promising one-point upper limits on the annihilation cross section. We show that by using the flux distribution at only one energy bin, one can probe the canonical cross section required for explaining the relic density, for dark matter of masses around tens of GeV.