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The photon spectrum emitted by a transrelativistic pair plasma is calculated in the presence of an ultrastrong magnetic field, and is shown to bear a remarkable resemblance to the rising hard X-ray spectra of quiescent magnetars. This emission is powered by pair annihilation which, in contrast with a weakly magnetized pair plasma, shows an extended low-frequency tail similar to bremsstrahlung. Cross sections for electron-positron annihilation/scattering, two-photon pair creation, and photon-$e^\pm$ scattering are adopted from our earlier ab initio QED calculations in the regime $10��_{\rm em}^{-1}B_{\rm Q} \gg B \gg B_{\rm Q}$. Careful attention is given to the $u$-channel scattering resonance. Magnetospheric arcades anchored in zones of intense crustal shear and extending to about twice the magnetar radius are identified as the sites of the persistent hard X-ray emission. We deduce a novel and stable configuration for the magnetospheric circuit, with a high plasma density sustained by ohmic heating and in situ pair creation. Pairs are sourced non-locally by photon collisions in zones with weak currents, such as the polar cap. Annihilation bremsstrahlung extends to the optical-IR band, where the plasma cutoff is located. The upper magnetar atmosphere experiences strong current-driven growth of ion-acoustic turbulence, which may limit positron diffusion. Coherent optical-IR emission is bounded near the observed flux by induced scattering. This model accommodates the rapid X-ray brightening of an activating magnetar, concentrated thermal hotspots, and the subdominant thermal X-ray emission of some active magnetars. Current injection is ascribed to continuous magnetic braiding, as seen in the global yielding calculations of Thompson, Yang & Ortiz., 28 pages, 18 figures, accepted for publication in the Astrophysical Journal after minor revisions

We evaluate several basic electrodynamic processes as modified by the presence of a very strong magnetic field, exceeding $B_{\rm Q} \equiv m^2/e = 4.4\times 10^{13}$ G. These results are needed to build models of dissipative phenomena outside magnetars and some other neutron stars. Differential and total cross sections and rates are presented for electron-photon scattering, the annihilation of an electron-positron pair into two photons, the inverse process of two-photon pair creation, and single-photon pair creation into the lowest Landau state. The relative importance of these interactions changes as the background magnetic field grows in strength. The particle phase space relevant for a given process may be restricted by single-photon pair creation, which also opens up efficient channels for pair multiplication, e.g. in combination with scattering. Our results are presented in the form of compact formulae that allow for relativistic electron (positron) motion, in the regime where Landau excitations can be neglected (corresponding to $10^3B_{\rm Q} \gg B \gg B_{\rm Q}$ for moderately relativistic motion along the magnetic field). Where a direct comparison is possible, our results are tested against earlier calculations, and a brief astrophysical context is provided. A companion paper considers electron-positron scattering, scattering of electrons and positrons by ions, and relativistic electron-ion bremsstrahlung., 28 pages and 12 figures, Astrophysical Journal 2018, 869, 44. Erratum added

This paper continues the approach of Kostenko \& Thompson to calculating quantum electrodynamic processes in the ultrastrong magnetic field near some neutron stars, such as magnetars or merging binary neutron stars. Here we consider electron-positron scattering, the Coulomb scattering of electrons and positrons off ions, and relativistic $e^\pm$-ion bremsstrahlung. The evaluation of differential and total cross sections simplifies considerably when the magnetic field lies in the range $10^3B_{\rm Q} \gg B \gg B_{\rm Q}$, where $B_{\rm Q} \equiv m^2/e = 4.4\times 10^{13}$ G. Then, relativistic motion of $e^\pm$ is possible even when restricted to the lowest Landau state. Accurate results for differential and total cross sections are obtained by truncating the sum over intermediate-state Landau levels and otherwise disregarding terms inversely proportional to the magnetic field, which are complicated enough to have inhibited previous attempts to calculate magnetic electron-positron scattering and relativistic bremsstrahlung. A quantitative account is made of the effects of Debye screening., 26 pages, 7 figures. Astrophysical Journal 2019, 875. Erratum added

In this review we consider in detail different theoretical topics associated with interaction in the dark sector. We study linear and nonlinear interactions which depend on the dark matter and dark energy densities. We consider a number of different models (including the holographic dark energy and dark energy in a fractal universe) with interacting dark energy (DE) and dark matter (DM), have done a thorough analysis of these models. The main task of this review was not only to give an idea about the modern set of different models of dark energy, but to show how much can be diverse dynamics of the universe in these models. We find that the dynamics of a Universe that contains interaction in the dark sector can differ significantly from the Standard Cosmological Model (SCM)., Comment: 132 pages, 32 figures. Submitted to International Journal of Modern Physics D