Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates

We present relativistic linear stability equations (RLSE) for quasi-relativistic cold atoms in a honeycomb optical lattice. These equations are derived from first principles and provide a method for computing stabilities of arbitrary localized solutions of the nonlinear Dirac equation (NLDE), a relativistic generalization of the nonlinear Schr\"odinger equation. We present a variety of such localized solutions: skyrmions, solitons, vortices, and half-quantum vortices, and study their stabilities via the RLSE. When applied to a uniform background, our calculations reveal an experimentally observable effect in the form of Cherenkov radiation. Remarkably, the Berry phase from the bipartite structure of the honeycomb lattice induces a boson-fermion transmutation in the quasi-particle operator statistics.Comment: 6 pages, 3 figure

Bogoliubov-Cerenkov radiation in a Bose-Einstein condensate flowing against an obstacle

We study the density modulation that appears in a Bose-Einstein condensate flowing with supersonic velocity against an obstacle. The experimental density profiles observed at JILA are reproduced by a numerical integration of the Gross-Pitaevskii equation and then interpreted in terms of Cerenkov emission of Bogoliubov excitations by the defect. The phonon and the single-particle regions of the Bogoliubov spectrum are respectively responsible for a conical wavefront and a fan-shaped series of precursors

Spatial distribution of Cherenkov radiation in periodic dielectric media

The nontrivial dispersion relation of a periodic medium affects both the spectral and the spatial distribution of Cherenkov radiation. We present a theory of the spatial distribution of Cherenkov radiation in the far-field zone inside arbitrary three- and two-dimensional dielectric media. Simple analytical expressions for the far-field are obtained in terms of the Bloch mode expansion. Numerical examples of the Cherenkov radiation in a two-dimensional photonic crystal is presented. The developed analytical theory demonstrates good agreement with numerically rigorous finite-difference time-domain calculations.Comment: 14 pages, 5 figures, Journal of Optics A (in press

Soliton form factors from lattice simulations

The form factor provides a convenient way to describe properties of topological solitons in the full quantum theory, when semiclassical concepts are not applicable. It is demonstrated that the form factor can be calculated numerically using lattice Monte Carlo simulations. The approach is very general and can be applied to essentially any type of soliton. The technique is illustrated by calculating the kink form factor near the critical point in 1+1-dimensional scalar field theory. As expected from universality arguments, the result agrees with the exactly calculable scaling form factor of the two-dimensional Ising model.Comment: 5 pages, 3 figures; v2: discussion extended, references added, version accepted for publication in PR

Macroscopic Geo-Magnetic Radiation Model; Polarization effects and finite volume calculations

An ultra-high-energy cosmic ray (UHECR) colliding with the Earth's atmosphere gives rise to an Extensive Air Shower (EAS). Due to different charge separation mechanisms within the thin shower front coherent electromagnetic radiation will be emitted within the radio frequency range. A small deviation of the index of refraction from unity will give rise to Cherenkov radiation up to distances of 100 meters from the shower core and therefore has to be included in a complete description of the radio emission from an EAS. Interference between the different radiation mechanisms, in combination with different polarization behavior will reflect in a lateral distribution function (LDF) depending on the orientation of the observer and a non-trivial fall-off of the radio signal as function of distance to the shower core.Comment: Proceedings of the ARENA2010 conference, Nantes, Franc

Cherenkov Radiation from e+e−e^+e^- Pairs and Its Effect on νe\nu_e Induced Showers

We calculate the Cherenkov radiation from an $e^+e^-$ pair at small separations, as occurs shortly after a pair conversion. The radiation is reduced (compared to that from two independent particles) when the pair separation is smaller than the wavelength of the emitted light. We estimate the reduction in light in large electromagnetic showers, and discuss the implications for detectors that observe Cherenkov radiation from showers in the Earth's atmosphere, as well as in oceans and Antarctic ice.Comment: Final version, with minor changes, to appear in PRD. 5 pages with 4 figure

Finite temperature Cherenkov radiation in the presence of a magnetodielectric medium

A canonical approach to Cherenkov radiation in the presence of a magnetodielectric medium is presented in classical, nonrelativistic and relativistic quantum regimes. The equations of motion for the canonical variables are solved explicitly for both positive and negative times. Maxwell and related constitute equations are obtained. In the large-time limit, the vector potential operator is found and expressed in terms of the medium operators. The energy loss of a charged particle, emitted in the form of radiation, in finite temperature is calculated. A Dirac equation concerning the relativistic motion of the particle in presence of the magnetodielectric medium is derived and the relativistic Cherenkov radiation at zero and finite temperature is investigated. Finally, it is shown that the Cherenkov radiation in nonrelativistic and relativistic quantum regimes, unlike its classical counterpart, introduces automatically a cutoff for higher frequencies beyond which the power of radiation emission is zero.Comment: To be appear in PR

Slow group velocity and Cherenkov radiation

We theoretically study the effect of ultraslow group velocities on the emission of Vavilov-Cherenkov radiation in a coherently driven medium. We show that in this case the aperture of the group cone on which the intensity of the radiation peaks is much smaller than that of the usual wave cone associated with the Cherenkov coherence condition. We show that such a singular behaviour may be observed in a coherently driven ultracold atomic gas.Comment: 4 pages, 4 figure

Formation of hard VHE gamma-ray spectra of blazars due to internal photon-photon absorption

The energy spectra of TeV gamma-rays from blazars, after being corrected for intergalatic absorption in the Extragalactic Background Light (EBL), appear unusually hard, a fact that poses challenges to the conventional models of particle acceleration in TeV blazars and/or to the EBL models. In this paper we show that the internal absorption of gamma-rays caused by interactions with dense narrow-band radiation fields in the vicinity of compact gamma-ray production regions can lead to the formation of gamma-ray spectra of an almost arbitrary hardness. This allows significant relaxation of the current tight constraints on particle acceleration and radiation models, although at the expense of enhanced requirements to the available nonthermal energy budget. The latter, however, is not a critical issue, as long as it can be largely compensated by the Doppler boosting, assuming very large ($\geq 30$) Doppler factors of the relativistically moving gamma-ray production regions. The suggested scenario of formation of hard gamma-ray spectra predicts detectable synchrotron radiation of secondary electron-positron pairs which might require a revision of the current ``standard paradigm'' of spectral energy distributions of gamma-ray blazars. If the primary gamma-rays are of hadronic origin related to $pp$ or $p \gamma$ interactions, the ``internal gamma-ray absorption'' model predicts neutrino fluxes close to the detection threshold of the next generation high energy neutrino detectors.Comment: 10 pages, 8 figures, submitted to MNRA