On the problem of relativistic particles motion in strong magnetic field and dense matter

We consider a problem of electron motion in different media and magnetic field. It is shown that in case of nonmoving medium and constant homogenious magnetic field the electron energies are quantized. We also discuss the general problem of eigenvectors and eigenvalues of a given class of Hamiltonians. We examine obtained exact solutions for the particular case of the electron motion in a rotating neutron star with account for matter and magnetic field effects. We argue that all of these considerations can be usefull for astrophysical applications

Polarization of the electron and positron produced in combined Coulomb and strong laser fields

The process of $e^+e^-$ production in the superposition of a Coulomb and a strong laser field is considered. The pair production rate integrated over the momentum and summed over the spin projections of one of the particles is derived exactly in the parameters of the laser field and in the Born approximation with respect to the Coulomb field. The case of a monochromatic circularly polarized laser field is considered in detail. A very compact analytical expression of the pair production rate and its dependence on the polarization of one of the created particles is obtained in the quasiclassical approximation for the experimentally relevant case of an undercritical laser field. As a result, the polarization of the created electron (positron) is derived.Comment: 16 pages, no figure

Hyperbolic carbon nanoforest for phase matching of ordinary and backward electromagnetic waves: second harmonic generation

We show that deliberately engineered dispersive metamaterial slab can enable the co-existence and phase matching of contra-propagating ordinary fundamental and extraordinary backward second harmonic surface electromagnetic modes. Energy flux and phase velocity are contra-directed in the backward waves which is the phenomenon that gives rise to unique nonlinear optical propagation processes. We show that frequencies, phase, and group velocities, as well as nanowaveguide losses inherent to the electromagnetic modes supported by such metamaterial, can be tailored to maximize conversion of frequencies and to reverse propagation direction of the generated wave. Such a possibility, which is of paramount importance for nonlinear photonics, is proved with a numerical model of the hyperbolic metamaterial made of carbon nanotubes standing on the metal surface. Extraordinary properties of the backward-wave second harmonic generation in the reflection direction and of the corresponding frequency doubling metareflector in the THz are investigated with a focus on the pulsed regime.Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:1602.0249

Pair Production Beyond the Schwinger Formula in Time-Dependent Electric Fields

We investigate electron-positron pair production in pulse-shaped electric background fields using a non-Markovian quantum kinetic equation. We identify a pulse-length range for subcritical fields still in the nonperturbative regime where the number of produced pairs significantly exceeds that of a naive expectation based on the Schwinger formula. From a conceptual viewpoint, we find a remarkable quantitative agreement between the (real-time) quantum kinetic approach and the (imaginary-time) effective action approach.Comment: 5 pages, 3 figures. Typos corrected and references added, PRD Versio

Practical analytical solutions for benchmarking of 2-D and 3-D geodynamic Stokes problems with variable viscosity

Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for benchmarking numerical codes aimed at modeling various mantle convection and lithospheric dynamics problems. The Main advantage of this new generalized approach is that a large variety of benchmark solutions can be generated, including relatively complex cases with open model boundaries, non-vertical gravity and variable gradients of the viscosity and density fields, which are not parallel to the Cartesian axes. Examples of respective 2-D and 3-D MatLab codes are provided with this paper

Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields

Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E_0 sech^2 (z/L), and in a temporally localized electric field such as E_0 sech^2 (t/T). The integration of the quadratic part of WKB instanton actions over the frequency and transverse momentum leads to the pair-production rate obtained by the worldline instanton method, including the prefactor, of Phys. Rev. D72, 105004 (2005) and D73, 065028 (2006). It is further shown that the WKB instanton action plus the next-to-leading order contribution in spinor QED equals the WKB instanton action in scalar QED, thus justifying why the WKB instanton in scalar QED can work for the pair production of fermions. Finally we obtain the pair-production rate in a spatially localized electric field together with a constant magnetic field in the same direction.Comment: RevTex, 12 pages, two figures; replaced by the version accepted in Phys. Rev.