We perform a complete calculation of electron-seeded pair creation (the trident process) in a constant crossed electromagnetic background. Unlike earlier treatments, we include the interference ...between exchange diagrams. We find that this exchange interference can be written as a contribution solely to the one-step process, and for small quantum nonlinearity parameter is of the same order as other one-step terms. We find that the exchange interference further suppresses the one-step process in this parameter regime. Our findings further support the crucial assumption made in laser-plasma simulation codes that at high intensities, the trident process can be well approximated by the repeated iteration of the single-vertex subprocesses. The applicability of this assumption to higher-vertex processes has fundamental importance to the development of simulation capabilities.
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By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is g = αχ2/3, where the ...dynamical quantum parameter χ = e√−(Fp)2/m3 combines the particle momentum p with the external field strength tensor F . Here we present and discuss the first nonperturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter g to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for g ≫ 1. Whereas the breakdown of perturbation theory occurs already for g ≳ 1, the leading-order result remains dominant until the asymptotic regime g ≫ 1 is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.
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An interface model of homogenization was proposed, this model considers the influence of the inclusions size of the micrometre range on the elastic properties of composites. The appearance of surface ...strains and shear stresses at the interphase boundary is associated with the "sticking" of the matrix to the surface of the inclusions. The effective modulus of elasticity of a composite is the sum of two terms: a constant part in the form of a modulus of elasticity of a bulk material, and a variable part that is caused by a shift at the interphase boundary and depends on the particles size. Absolute of particles sizes were considered by introducing within the interfacial model empirical elasticity modulus of the composite with the one basic particle size. The results of the calculation are in good agreement with the experimental data for Young's modulus of polymer composites with spherical particles.
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4.
Toroidal Dipolar Response in a Metamaterial Kaelberer, T; Fedotov, V.A; Papasimakis, N ...
Science (American Association for the Advancement of Science),
12/2010, Volume:
330, Issue:
6010
Journal Article
Peer reviewed
Open access
Toroidal multipoles are fundamental electromagnetic excitations different from those associated with the familiar charge and magnetic multipoles. They have been held responsible for parity violation ...in nuclear and particle physics, but direct evidence of their existence in classical electrodynamics has remained elusive. We report on the observation of a resonant electromagnetic response in an artificially engineered medium, or metamaterial, that cannot be attributed to magnetic or charge multipoles and can only be explained by the existence of a toroidal dipole. Our direct experimental evidence of the toroidal response brings attention to the often ignored electromagnetic interactions involving toroidal multipoles, which could be present in naturally occurring systems, especially at the macromolecule level, where toroidal symmetry is ubiquitous.
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The toroidal dipole is a peculiar electromagnetic excitation that can not be presented in terms of standard electric and magnetic multipoles. A static toroidal dipole has been shown to lead to ...violation of parity in atomic spectra and many other unusual electromagnetic phenomena. The existence of electromagnetic resonances of toroidal nature was experimentally demonstrated only recently, first in the microwave metamaterials, and then at optical frequencies, where they could be important in spectroscopy analysis of a wide class of media with constituents of toroidal symmetry, such as complex organic molecules, fullerenes, bacteriophages, etc. Despite the experimental progress in studying toroidal resonances, no direct link has yet been established between microscopic toroidal excitations and macroscopic scattering characteristics of the medium. To address this essential gap in the electromagnetic theory, we have developed an analytical approach for calculating the transmissivity and reflectivity of thin slabs of materials that exhibit toroidal dipolar excitations.
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The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the ...magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion and optical activity. Toroidal excitations also exist in free space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating charge-current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal excitations can have important implications for the fields of photonics, sensing, energy and information.
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Abstract
Using a quasi-static model of a toroidal metamaterial we demonstrate analytically that simultaneous excitation of the magnetic and toroidal dipoles in an array of subwavelength toroidal ...solenoids results in gyrotropic behaviour resembling conventional optical activity. We derive the polarization eigenstates of this uniaxial chiral toroidal metamaterial and show that such a medium is reciprocal, while the eigenstates are represented by two counter-rotating ellipses, one of which can be used for probing changes of the host permittivity in a manner exclusive to the toroidal metamaterial. We also show that the mechanism of permittivity sensing involving resonant toroidal response is fundamentally different from that, which has been exploited so far under the term ‘toroidal’.
For a one-dimensional difference Schrödinger equation, we obtain uniform semiclassical asymptotic formulas for the transition matrix between basis solutions having simple asymptotic behavior in ...domains separated by two close turning points. We use no information on the behavior of the solutions near the turning points. Our method can be applied to a wide class of problems.
DOI 10.1134/S1061920822040069
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The survey is devoted to the complex WKB method which arose as an approach to describing the asymptotic behavior of solutions to one-dimensional ordinary differential equations with semiclassical ...parameter on the complex plane. Later this method was generalized to the case of difference equations. Related constructions arose when studying exponentially small effects in the problem concerning the adiabatic perturbation of the one-dimensional periodic Schrödinger operator. All these three branches of the method are discussed in the survey from a unified position. The main constructions of the method are described and the proofs are either provided or their ideas are described in detail. Some new finds are published for the first time.
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