The production of electron-positron pairs from vacuum by counterpropagating laser beams of linear polarization is calculated. In contrast to the usual approximate approach, the spatial dependence and magnetic component of the laser field are taken into account. We show that the latter strongly affects the creation process at high laser frequency: the production probability is reduced, the kinematics is fundamentally modified, the resonant Rabi-oscillation pattern is distorted and the resonance positions are shifted, multiplied and split. PACS numbers: 42.50.Hz;42.55.Vc;12.20.Ds In the presence of very strong electromagnetic fields the quantum electrodynamic vacuum becomes unstable and decays into electron-positron (e + e − ) pairs [1]. This phenomenon has been realized experimentally, e.g., in relativistic heavy-ion collisions [2]. Shortly after the invention of the laser almost 50 years ago, theoreticians began to study e + e − pair production by intense laser light [3]. Because of the remarkable progress in laser technology during recent years, the interest in the process has been revived since an experimental investigation of pair creation by pure laser light is coming into reach. The only observation of laser-induced pair production until now was accomplished ten years ago at SLAC (Stanford, California), where a 46 GeV electron beam was brought into collision with an intense optical laser pulse [4]. In this experiment, a γ-photon produced via Compton scattering or the electron Coulomb field assisted the laser beam in the pair production.The most simple field configuration for realization of purely laser-induced pair production consists of two counterpropagating laser pulses of equal frequency and intensity (see [5,6,7,8] and references therein). The resulting standing wave is inhomogeneous both in time and in space which represents a formidable task for the nonperturbative quantum field theory, see e.g. [9]. All theoretical investigations so far have approximated the standing laser wave by a spatially homogeneous electric field oscillating in time. This dipole approximation is expected to be well-justified in optical laser fields, where the wavelength is much larger than the typical length scale of the process: λ ≫ l ∼ 2m/(|e|E) in natural units ( = c = 1) which are employed throughout. In terms of the relativistic parameter ξ = |e|E/(mω), this relation corresponds to ξ ≫ 1. Here E and ω are the laser field and its frequency, e and m the electron charge and mass, respectively. Meanwhile the experimental realization of laser-induced pair production is also extensively discussed in connection with upcoming x-ray freeelectron laser (XFEL) facilities [7,8]. In this case, however, the laser frequency is high, ξ 1 and the magnetic field component is not negligible. The latter, in general, can have an important influence on the pair creation process. This is most evidently demonstrated by the fact that a single plane laser wave cannot extract pairs from the vacuum, whereas a purely electric field can. In this Le...

No abstract

Abstract. We study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small parameter ε and the magnets as classical ±1 spin variables interacting via an Ising type energy. Under surface scaling of the energy we prove, in terms of Γ-convergence that, up to subsequences, the (continuum) Γ-limit of these energies is finite on the set of Caccioppoli partitions representing the magnetic Weiss domains where it has a local integral structure. Assuming stationarity of the stochastic lattice, we can make use of ergodic theory to further show that the Γ-limit exists and that the integrand is given by an asymptotic homogenization formula which becomes deterministic if the lattice is ergodic.

We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By Γ -convergence we derive a one-dimensional limit theory and show that isolated local minimizers of the limit model can be approached by local minimizers of the three-dimensional model. In the case of isotropic materials and for two-layers prestrained three-dimensional models the limit energy further simplifies to that of a Kirchhoff rod-model of an intrinsically curved beam. In this case we study the limit theory and investigate global and/or local stability of straight and helical configurations. Through some simple simulations we finally compare our results with real experiments. arXiv:1606.04524v1 [math.AP] 14 Jun 2016 2 MARCO CICALESE, MATTHIAS RUF, AND FRANCESCO SOLOMBRINO been derived since the pioneering papers by Le Dret and Raoult [16] and by Friesecke, James and Müller [11,12] by many authors [1,27,28,29,33,34] under different modelling assumptions.More recently the problem above has gained increasing attention in the case of prestrained bodies. A number of results have appeared in the case of 3-d to 2-d dimension reduction in [4,10,17,18,35] and many interesting questions have been raised. On one hand the above problem has been left undiscussed in the case of 3-d to 1-d dimension reduction (see [2,3] for a similar problem in the theory of nematic elastomers where the dimension reduction is performed in two subsequent steps 3-d to 2-d and 2-d to 1-d), on the other hand recent experiments in [19] suggest to consider it from a rigorous mathematical point of view. In few words in [19] the authors take two long strips of elastomer of the same initial width, but unequal length. The short strip is stretched uniaxially to be equal in length to the longer one. The initial heights are chosen so that after stretching the bi-strip system has a rectangular cross section. The two strips are then glued together side-by-side along their length. The bi-strips appear flat and the initially shorter strip is under a uniaxial prestrain. As a last step of the experiment, the external force needed to stretch the ends of the bi-strip is gradually released so that the initially flat bistrip starts to bend and twist out of plane. It may evolve towards either a helical or hemihelical shape (more complex structure in which helices with different chiralities seem to periodically alternate), depending on the cross-sectional aspect ratio. In particular, a big enough aspect ratio favors the formation of a helix, whereas a small aspect ratio favors that of a hemihelix.The analysis in [19] is simplified first assuming that the system is one-dimensional, so that a Kirchhoff-rod approximation is used, and then analyzing stability of configurations close to the straight rod by matching asymptotics in a restricted class of competitors. On one hand the results appear to be mathematically unsatisfying, on the other hand a rigorous derivation of the complete observed behavior seems to be...

a b s t r a c tThe Klein-Gordon equation is a Lorentz invariant equation of motion for spinless particles. We propose a real space split operator method for the solution of the time-dependent Klein-Gordon equation with arbitrary electromagnetic fields. Split operator methods for the Schrödinger equation and the Dirac equation typically operate alternately in real space and momentum space and, therefore, require the computation of a Fourier transform in each time step. However, the fact that the kinetic energy operator b K in the two-component representation of the Klein-Gordon equation is a nilpotent operator, that is b K 2 ¼ 0, allows us to implement the split operator method for the Klein-Gordon equation entirely in real space. Consequently, the split operator method for the Klein-Gordon equation does not require the computation of a Fourier transform and may be parallelized efficiently by domain decomposition.