58,079 research outputs found
Continuous functions with universally divergent Fourier series on small subsets of the circle
It is shown that quasi all continuous functions on the unit circle have the
property that, for many small subsets E of the circle, the partial sums of
their Fourier series considered as functions restricted to E exhibit certain
universality properties.Comment: 6 page
Spin effects in strong-field laser-electron interactions
The electron spin degree of freedom can play a significant role in
relativistic scattering processes involving intense laser fields. In this
contribution we discuss the influence of the electron spin on (i) Kapitza-Dirac
scattering in an x-ray laser field of high intensity, (ii) photo-induced
electron-positron pair production in a strong laser wave and (iii) multiphoton
electron-positron pair production on an atomic nucleus. We show that in all
cases under consideration the electron spin can have a characteristic impact on
the process properties and their total probabilities. To this end,
spin-resolved calculations based on the Dirac equation in the presence of an
intense laser field are performed. The predictions from Dirac theory are also
compared with the corresponding results from the Klein-Gordon equation.Comment: 9 pages, 6 figure
Symmetries and Triplet Dispersion in a Modified Shastry-Sutherland Model for SrCu_2(BO_3)_2
We investigate the one-triplet dispersion in a modified Shastry-Sutherland
Model for SrCu_2(BO_3)_2 by means of a series expansion about the limit of
strong dimerization. Our perturbative method is based on a continuous unitary
transformation that maps the original Hamiltonian to an effective, energy
quanta conserving block diagonal Hamiltonian H_{eff}. The dispersion splits
into two branches which are nearly degenerated. We analyse the symmetries of
the model and show that space group operations are necessary to explain the
degeneracy of the dispersion at k=0 and at the border of the magnetic Brillouin
zone. Moreover, we investigate the behaviour of the dispersion for small |k|
and compare our results to INS data.Comment: 9 pages, 8 figures accepted by J. Phys.: Condens. Matte
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