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Trace formulae for three-dimensional hyperbolic lattices and application to a strongly chaotic tetrahedral billiard
This paper is devoted to the quantum chaology of three-dimensional systems. A
trace formula is derived for compact polyhedral billiards which tessellate the
three-dimensional hyperbolic space of constant negative curvature. The exact
trace formula is compared with Gutzwiller's semiclassical periodic-orbit theory
in three dimensions, and applied to a tetrahedral billiard being strongly
chaotic. Geometric properties as well as the conjugacy classes of the defining
group are discussed. The length spectrum and the quantal level spectrum are
numerically computed allowing the evaluation of the trace formula as is
demonstrated in the case of the spectral staircase N(E), which in turn is
successfully applied in a quantization condition.Comment: 32 pages, compressed with gzip / uuencod
Can one reconstruct masked CMB sky?
The CMB maps obtained by observations always possess domains which have to be
masked due to severe uncertainties with respect to the genuine CMB signal.
Cosmological analyses ideally use full CMB maps in order to get e.g. the
angular power spectrum. There are attempts to reconstruct the masked regions at
least at low resolutions, i.e. at large angular scales, before a further
analysis follows. In this paper, the quality of the reconstruction is
investigated for the ILC (7yr) map as well as for 1000 CMB simulations of the
LambdaCDM concordance model. The latter allows an error estimation for the
reconstruction algorithm which reveals some drawbacks. The analysis points to
errors of the order of a significant fraction of the mean temperature
fluctuation of the CMB. The temperature 2-point correlation function C(theta)
is evaluated for different reconstructed sky maps which leads to the conclusion
that it is safest to compute it on the cut-sky
Cosmic Topology of Polyhedral Double-Action Manifolds
A special class of non-trivial topologies of the spherical space S^3 is
investigated with respect to their cosmic microwave background (CMB)
anisotropies. The observed correlations of the anisotropies on the CMB sky
possess on large separation angles surprising low amplitudes which might be
naturally be explained by models of the Universe having a multiconnected
spatial space. We analysed in CQG 29(2012)215005 the CMB properties of prism
double-action manifolds that are generated by a binary dihedral group D^*_p and
a cyclic group Z_n up to a group order of 180. Here we extend the CMB analysis
to polyhedral double-action manifolds which are generated by the three binary
polyhedral groups (T^*, O^*, I^*) and a cyclic group Z_n up to a group order of
1000. There are 20 such polyhedral double-action manifolds. Some of them turn
out to have even lower CMB correlations on large angles than the Poincare
dodecahedron
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