Simple analytical approximations for treatment of inverse Compton scattering of relativistic electrons in the black-body radiation field

The inverse Compton (IC) scattering of relativistic electrons is one of the major gamma-ray production mechanisms in different environments. Often the target photons for the IC scattering are dominated by black (or grey) body radiation. In this case, the precise treatment of the characteristics of IC radiation requires numerical integrations over the Planckian distribution. Formally, analytical integrations are also possible but they result in series of several special functions; this limits the efficiency of usage of these expressions. The aim of this work is the derivation of approximate analytical presentations which would provide adequate accuracy for the calculations of the energy spectra of up-scattered radiation, the rate of electron energy losses, and the mean energy of emitted photons. Such formulae have been obtained by merging the analytical asymptotic limits. The coefficients in these expressions are calculated via the least square fitting of the results of numerical integrations. The simple analytical presentations, obtained for both the isotropic and anisotropic target radiation fields, provide adequate (as good as $1\%$) accuracy for broad astrophysical applications.Comment: 16 pages, 11 figures, accepted for publication in Ap

Thermal out-of-time-order correlators, KMS relations, and spectral functions

We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in the larger context of out-of-time-ordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with time-reversal to stay within the purview of Schwinger-Keldysh functional integrals, we show that there is a natural way to phrase them directly in terms of OTO correlators. We use these observations to construct a natural causal basis for thermal n-point functions in terms of fully nested commutators. We provide several general results which can be inferred from cyclic orbits of permutations, and exemplify the abstract results using a quantum oscillator as an explicit example.Comment: 36 pages + appendices. v2: minor changes + refs added. v3: minor changes, published versio

A Time Independent Energy Estimate for Outgoing Scalar Waves in the Kerr Geometry

The Cauchy problem for the scalar wave equation in the Kerr geometry is considered, with initial data which is smooth and compactly supported outside the event horizon. A time-independent energy estimate for the outgoing wave is obtained. As an application we estimate the outgoing energy for wave-packet initial data, uniformly as the support of the initial data is shifted to infinity. The main mathematical tool is our previously derived integral representation of the wave propagator.Comment: 31 pages, LaTeX, minor changes (published version

So Far so Good: Age, Happiness, and Relative Income

In a simple 2-period model of relative income under uncertainty, higher comparison income for the younger cohort can signal higher or lower expected lifetime relative income, and hence either increase or decrease well-being. With data from the German Socio-Economic Panel and the British Household Panel Survey, we first confirm the standard negative effects of comparison income on life satisfaction with all age groups, and many controls. However when we split the West German sample by age we find a positive significant effect of comparison income in the under 45s, and the usual negative effect only in the over 45 group. With the same split in UK and East German data, comparison income loses significance, which is consistent with the model prediction for the younger group. Our results provide first evidence that the standard aggregation with only a quadratic control for age can obscure major differences in the effects of relative income.Subjective life-satisfaction, comparison income, reference groups, age, welfare

Non-Contact Measurement of Thermal Diffusivity in Ion-Implanted Nuclear Materials

Knowledge of mechanical and physical property evolution due to irradiation damage is essential for the development of future fission and fusion reactors. Ion-irradiation provides an excellent proxy for studying irradiation damage, allowing high damage doses without sample activation. Limited ion-penetration-depth means that only few-micron-thick damaged layers are produced. Substantial effort has been devoted to probing the mechanical properties of these thin implanted layers. Yet, whilst key to reactor design, their thermal transport properties remain largely unexplored due to a lack of suitable measurement techniques. Here we demonstrate non-contact thermal diffusivity measurements in ion-implanted tungsten for nuclear fusion armour. Alloying with transmutation elements and the interaction of retained gas with implantation-induced defects both lead to dramatic reductions in thermal diffusivity. These changes are well captured by our modelling approaches. Our observations have important implications for the design of future fusion power plants.Comment: 15 pages, 3 figure

Production of TeV gamma-radiation in the vicinity of the supermassive black hole in the giant radiogalaxy M87

Although the giant radiogalaxy M 87 harbors many distinct regions of broad-band nonthermal emission, the recently reported fast variability of TeV gamma rays from M 87 on a timescale of days strongly constrains the range of speculations concerning the possible sites and scenarios of particle acceleration responsible for the observed TeV emission. A natural production site of this radiation is the immediate vicinity of the central supermassive mass black hole (BH). Because of the low bolometric luminosity, the nucleus of M 87 is effectively transparent for gamma rays up to energy of 10 TeV, which makes this source an ideal laboratory for study of particle acceleration processes close to the BH event horizon. We critically analyse different possible radiation mechanisms in this region, and argue that the observed very high-energy gamma ray emission can be explained by the inverse Compton emission of ultrarelativistic electron-positron pairs produced through the development of an electromagnetic cascade in the BH magnetosphere. We demonstrate, through detailed numerical calculations of acceleration and radiation of electrons in the magnetospheric vacuum gap, that this ``pulsar magnetosphere like'' scenario can satisfactorily explain the main properties of TeV gamma-ray emission of M 87.Comment: 11 pages, ApJ, in prin

Polymer state approximations of Schroedinger wave functions

It is shown how states of a quantum mechanical particle in the Schroedinger representation can be approximated by states in the so-called polymer representation. The result may shed some light on the semiclassical limit of loop quantum gravity.Comment: 11 pages, 1 figure, Conclusions section adde

B -> pi pi, New Physics in B -> pi K and Implications for Rare K and B Decays

The measured B -> pi pi, pi K branching ratios exhibit puzzling patterns. We point out that the B -> pi pi hierarchy can be nicely accommodated in the Standard Model (SM) through non-factorizable hadronic interference effects, whereas the B -> pi K system may indicate new physics (NP) in the electroweak (EW) penguin sector. Using the B -> pi pi data and the SU(3) flavour symmetry, we may fix the hadronic B -> pi K parameters, which allows us to show that any currently observed feature of the B -> pi K system can be easily explained through enhanced EW penguins with a large CP-violating NP phase. Restricting ourselves to a specific scenario, where NP enters only through Z^0 penguins, we derive links to rare K and B decays, where an enhancement of the K_L-> pi^0 nu nu_bar rate by one order of magnitude, with BR(K_L -> pi^0 nu nu_bar) > BR(K^+ -> pi^+ nu nu_bar), BR(K_L -> pi^0 e^+ e^-)=O(10^{-10}), (\sin2\beta)_{pi nu nu_bar} K* mu^+ mu^-, are the most spectacular effects. We address also other rare K and B decays, epsilon'/epsilon and B_d -> phi K_S.Comment: 6 pages, LaTeX, reference added and a few typos correced, to appear in Physical Review Letter

Gamma ray emission and stochastic particle acceleration in galaxy clusters

FERMI (formely GLAST) will shortly provide crucial information on relativistic particles in galaxy clusters. We discuss non-thermal emission in the context of general calculations in which relativistic particles (protons and secondary electrons due to proton-proton collisions) interact with MHD turbulence generated in the cluster volume during cluster mergers. Diffuse cluster-scale radio emission (Radio Halos) and hard X-rays are produced during massive mergers while gamma ray emission, at some level, is expected to be common in galaxy clusters.Comment: 4 pages, 2 Figure, proc. of the 4th Heidelberg International Symposium on High Energy Gamma-ray Astronom