3,724 research outputs found
Exact solution of the Zeeman effect in single-electron systems
Contrary to popular belief, the Zeeman effect can be treated exactly in
single-electron systems, for arbitrary magnetic field strengths, as long as the
term quadratic in the magnetic field can be ignored. These formulas were
actually derived already around 1927 by Darwin, using the classical picture of
angular momentum, and presented in their proper quantum-mechanical form in 1933
by Bethe, although without any proof. The expressions have since been more or
less lost from the literature; instead, the conventional treatment nowadays is
to present only the approximations for weak and strong fields, respectively.
However, in fusion research and other plasma physics applications, the magnetic
fields applied to control the shape and position of the plasma span the entire
region from weak to strong fields, and there is a need for a unified treatment.
In this paper we present the detailed quantum-mechanical derivation of the
exact eigenenergies and eigenstates of hydrogen-like atoms and ions in a static
magnetic field. Notably, these formulas are not much more complicated than the
better-known approximations. Moreover, the derivation allows the value of the
electron spin gyromagnetic ratio to be different from 2. For
completeness, we then review the details of dipole transitions between two
hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various
approximations made in the derivation are also discussed in details.Comment: 18 pages, 4 figures. Submitted to Physica Script
Rosenbrock time integration for unsteady flow simulations
This contribution compares the efficiency of Rosenbrock time integration
schemes with ESDIRK schemes, applicable to unsteady flow and fluid-structure interaction
simulations. Compared to non-linear ESDIRK schemes, the linear implicit Rosenbrock-
Wanner schemes require subsequent solution of the same linear systems with different
right hand sides. By solving the linear systems with the iterative solver GMRES, the preconditioner
can be reused for the subsequent stages of the Rosenbrock-Wanner scheme.
Unsteady flow simulations show a gain in computational efficiency of approximately factor
three to five in comparison with ESDIRK
Determination of the trap-assisted recombination strength in polymer light emitting diodes
The recombination processes in poly(p-phenylene vinylene) based polymer light-emitting diodes (PLEDs) are investigated. Photogenerated current measurements on PLED device structures reveal that next to the known Langevin recombination also trap-assisted recombination is an important recombination channel in PLEDs, which has not been considered until now. The dependence of the open-circuit voltage on light intensity enables us to determine the strength of this process. Numerical modeling of the current-voltage characteristics incorporating both Langevin and trap-assisted recombination yields a correct and consistent description of the PLED, without the traditional correction of the Langevin prefactor. At low bias voltage the trap-assisted recombination rate is found to be dominant over the free carrier recombination rate.
Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach
We consider the Langevin equation with multiplicative noise term which
depends on time and space. The corresponding Fokker-Planck equation in
Stratonovich approach is investigated. Its formal solution is obtained for an
arbitrary multiplicative noise term given by , and the
behaviors of probability distributions, for some specific functions of %
, are analyzed. In particular, for , the physical
solutions for the probability distribution in the Ito, Stratonovich and
postpoint discretization approaches can be obtained and analyzed.Comment: 6 pages in LATEX cod
Confluence reduction for Markov automata
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude
Origin of the dark-current ideality factor in polymer:fullerene bulk heterojunction solar cells
Universal strategy for Ohmic hole injection into organic semiconductors with high ionization energies
The Diffuse Gamma-Ray Background from Supernovae
The Cosmic Gamma-ray Background (CGB) in the MeV region is believed to be due
to photons from radioactivity produced in SNe throughout the history of
galaxies in the universe. In particular, gamma-ray line emission from the decay
chain 56Ni-> 56Co->56Fe provides the dominant photon source. Although iron
synthesis occurs in all types of SNe, the contribution to the CGB is dominated
by SNIa events due to their higher photon escape probabilities. Estimates of
the star formation history in the universe suggest a rapid increase by a factor
\~ 10 from the present to a redshift z_p ~ 1.5, beyond which it either remains
constant or decreases slowly. We integrate the observed star formation history
to determine the CGB from the corresponding SN rate history. In addition to
gamma-rays from short-lived radioactivity in SNIa and SNII/Ibc we also
calculate the minor contributions from long-lived radioactivities (26Al, 44Ti,
60Co, and electron-positron pair annihilation). Although progenitor evolution
for SNIa is not yet fully understood, various arguments suggest delays of order
1-2 Gy between star formation and the production of SNIa's. The effect of this
delay on the CGB is discussed. We emphasize the value of gamma-ray observations
of the CGB in the MeV range as an independent tool for studies of the cosmic
star formation history. If the delay between star formation and SNIa activity
exceeds 1 Gy substantially, and/or the peak of the cosmic star formation rate
occurs at a redshift much larger than unity, the gamma-ray production of SNIa
would be insufficient to explain the observed CGB. Alternatively, the cosmic
star formation rate would have to be higher (by a factor 2-3) than commonly
assumed, which is in accord with several upward revisions reported in the
recent literature.Comment: Minor changes, 26 pages, 9 figures, Accepted by Ap
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