232 research outputs found
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
Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions
In the relativistic and the nonrelativistic theoretical treatment of moderate
and high-power laser-matter interaction, the generalized Bessel function occurs
naturally when a Schr\"odinger-Volkov and Dirac-Volkov solution is expanded
into plane waves. For the evaluation of cross sections of quantum
electrodynamic processes in a linearly polarized laser field, it is often
necessary to evaluate large arrays of generalized Bessel functions, of
arbitrary index but with fixed arguments. We show that the generalized Bessel
function can be evaluated, in a numerically stable way, by utilizing a
recurrence relation and a normalization condition only, without having to
compute any initial value. We demonstrate the utility of the method by
illustrating the quantum-classical correspondence of the Dirac-Volkov solutions
via numerical calculations.Comment: 14 pages, 5 figure
Simulation of stochastic reaction-diffusion processes on unstructured meshes
Stochastic chemical systems with diffusion are modeled with a
reaction-diffusion master equation. On a macroscopic level, the governing
equation is a reaction-diffusion equation for the averages of the chemical
species. On a mesoscopic level, the master equation for a well stirred chemical
system is combined with Brownian motion in space to obtain the
reaction-diffusion master equation. The space is covered by an unstructured
mesh and the diffusion coefficients on the mesoscale are obtained from a finite
element discretization of the Laplace operator on the macroscale. The resulting
method is a flexible hybrid algorithm in that the diffusion can be handled
either on the meso- or on the macroscale level. The accuracy and the efficiency
of the method are illustrated in three numerical examples inspired by molecular
biology
Effect of a strong laser field on 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
A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems
We derive a posteriori error bounds for a quasilinear parabolic problem,
which is approximated by the -version interior penalty discontinuous
Galerkin method (IPDG). The error is measured in the energy norm. The theory is
developed for the semidiscrete case for simplicity, allowing to focus on the
challenges of a posteriori error control of IPDG space-discretizations of
strictly monotone quasilinear parabolic problems. The a posteriori bounds are
derived using the elliptic reconstruction framework, utilizing available a
posteriori error bounds for the corresponding steady-state elliptic problem.Comment: 8 pages, conference ENUMATH 200
Triple Compton effect: A photon splitting into three upon collision with a free electron
The process in which a photon splits into three after the collision with a
free electron (triple Compton effect) is the most basic process for the
generation of a high-energy multi-particle entangled state composed out of
elementary quanta. The cross section of the process is evaluated in two
experimentally realizable situations, one employing gamma photons and
stationary electrons, and the other using keV photons and GeV electrons of an
x-ray free electron laser. For the first case, our calculation is in agreement
with the only available measurement of the differential cross section for the
process under study. Our estimates indicate that the process should be readily
measurable also in the second case. We quantify the polarization entanglement
in the final state by a recently proposed multi-particle entanglement measure.Comment: 5 pages; RevTeX; to be published in Phys.Rev.Let
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