Theoretical study of the Compton effect with correlated three-photon emission: From the differential cross section to high-energy triple-photon entanglement

The three-photon Compton effect is studied. An incoming photon undergoes triple scattering off a free electron, which leads to the emission of three entangled photons. We investigate the properties of both the total cross section, assuming a low-energy cutoff for the detected photons, and the differential cross section. Particular emphasis is laid on evaluating polarization-resolved cross sections. The entanglement of the final three-photon state is analyzed.Comment: 14 pages; RevTe

Effect of a strong laser field on e+e−e^+ e^- photoproduction by relativistic nuclei

We study the influence of a strong laser field on the Bethe-Heitler photoproduction process by a relativistic nucleus. The laser field propagates in the same direction as the incoming high-energy photon and it is taken into account exactly in the calculations. Two cases are considered in detail. In the first case, the energy of the incoming photon in the nucleus rest frame is much larger than the electron's rest energy. The presence of the laser field may significantly suppress the photoproduction rate at soon available values of laser parameters. In the second case, the energy of the incoming photon in the rest frame of the nucleus is less than and close to the electron-positron pair production threshold. The presence of the laser field allows for the pair production process and the obtained electron-positron rate is much larger than in the presence of only the laser and the nuclear field. In both cases we have observed a strong dependence of the rate on the mutual polarization of the laser field and of the high-energy photon and the most favorable configuration is with laser field and high-energy photon linearly polarized in the same direction. The effects discussed are in principle measurable with presently available proton accelerators and laser systems.Comment: 21 pages, 4 figure

Barrier control in tunneling e^+ e^- photoproduction

Tunneling electron-positron pair production is studied in a new setup in which a strong low-frequency and a weak high-frequency laser field propagate in the same direction and collide head-on with a relativistic nucleus. The electron-positron pair production rate is calculated analytically in the limit in which in the nucleus rest frame the strong field is undercritical and the frequency of the weak field is below and close to the pair production threshold. By changing the frequency of the weak field one can reduce the tunneling barrier substantially. As a result tunneling pair production is shown to be observable with presently available technology.Comment: 4 pages, 3 figure

Numerical calculation of Bessel, Hankel and Airy functions

The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument is to be evaluated. The coefficients in the well-known uniform asymptotic expansions have a complex mathematical structure which involves Airy functions. For Bessel and Hankel functions, we present an adapted algorithm which relies on a combination of three methods: (i) numerical evaluation of Debye polynomials, (ii) calculation of Airy functions with special emphasis on their Stokes lines, and (iii) resummation of the entire uniform asymptotic expansion of the Bessel and Hankel functions by nonlinear sequence transformations. In general, for an evaluation of a special function, we advocate the use of nonlinear sequence transformations in order to bridge the gap between the asymptotic expansion for large argument and the Taylor expansion for small argument ("principle of asymptotic overlap"). This general principle needs to be strongly adapted to the current case, taking into account the complex phase of the argument. Combining the indicated techniques, we observe that it possible to extend the range of applicability of existing algorithms. Numerical examples and reference values are given.Comment: 18 pages; 7 figures; RevTe

Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A + B -> C, or A + A -> C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site).Comment: 33 pages, submitted to Physical Biolog

An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials

A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics (2011

Enhanced ionization of acetylene in intense laser pulses is due to energy upshift and field coupling of multiple orbitals

Synopsis We describe a new enhanced ionization mechanism for polyatomic molecules. It works via a significant energy up-shift of valence orbitals for stretched bonds and a strong concomitant increase in the coupling between multiple molecular orbitals

Dynamically coupling full Stokes and shallow shelf approximation for marine ice sheet flow using Elmer/Ice (v8.3)

Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve due to the nonlinearity introduced by the rheology. Therefore, approximations to the FS equations are commonly used, especially when modeling a marine ice sheet (ice sheet, ice shelf, and/or ice stream) for 103 years or longer. The shallow ice approximation (SIA) and shallow shelf approximation (SSA) are commonly used but are accurate only for certain parts of an ice sheet. Here, we report a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS–SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5&thinsp;% for diagnostic runs and below 5&thinsp;% for prognostic runs. Results for grounding line dynamics obtained with the FS–SSA coupling are similar to those obtained from an FS model in an experiment with a periodical temperature forcing over 3000 years that induces grounding line advance and retreat. The rapid convergence of the FS–SSA coupling shows a large potential for reducing computation time, such that modeling a marine ice sheet for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced by 32&thinsp;%, when the coupling is applied to a 3-D ice shelf.</p