648 research outputs found
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
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
Dodecahedral topology fails to explain quadrupole-octupole alignment
The CMB quadrupole and octupole, as well as being weaker than expected, align
suspiciously well with each other. Non-trivial spatial topology can explain the
weakness. Might it also explain the alignment? The answer, at least in the case
of the Poincare dodecahedral space, is a resounding no.Comment: 5 pages, 1 figur
Cosmic microwave anisotropies in an inhomogeneous compact flat universe
The anisotropies of the cosmic microwave background (CMB) are computed for
the half-turn space E_2 which represents a compact flat model of the Universe,
i.e. one with finite volume. This model is inhomogeneous in the sense that the
statistical properties of the CMB depend on the position of the observer within
the fundamental cell. It is shown that the half-turn space describes the
observed CMB anisotropies on large scales better than the concordance model
with infinite volume. For most observer positions it matches the temperature
correlation function even slightly better than the well studied 3-torus
topology
How well-proportioned are lens and prism spaces?
The CMB anisotropies in spherical 3-spaces with a non-trivial topology are
analysed with a focus on lens and prism shaped fundamental cells. The
conjecture is tested that well proportioned spaces lead to a suppression of
large-scale anisotropies according to the observed cosmic microwave background
(CMB). The focus is put on lens spaces L(p,q) which are supposed to be oddly
proportioned. However, there are inhomogeneous lens spaces whose shape of the
Voronoi domain depends on the position of the observer within the manifold.
Such manifolds possess no fixed measure of well-proportioned and allow a
predestined test of the well-proportioned conjecture. Topologies having the
same Voronoi domain are shown to possess distinct CMB statistics which thus
provide a counter-example to the well-proportioned conjecture. The CMB
properties are analysed in terms of cyclic subgroups Z_p, and new point of view
for the superior behaviour of the Poincar\'e dodecahedron is found
Spectral Statistics in the Quantized Cardioid Billiard
The spectral statistics in the strongly chaotic cardioid billiard are
studied. The analysis is based on the first 11000 quantal energy levels for odd
and even symmetry respectively. It is found that the level-spacing distribution
is in good agreement with the GOE distribution of random-matrix theory. In case
of the number variance and rigidity we observe agreement with the random-matrix
model for short-range correlations only, whereas for long-range correlations
both statistics saturate in agreement with semiclassical expectations.
Furthermore the conjecture that for classically chaotic systems the normalized
mode fluctuations have a universal Gaussian distribution with unit variance is
tested and found to be in very good agreement for both symmetry classes. By
means of the Gutzwiller trace formula the trace of the cosine-modulated heat
kernel is studied. Since the billiard boundary is focusing there are conjugate
points giving rise to zeros at the locations of the periodic orbits instead of
exclusively Gaussian peaks.Comment: 20 pages, uu-encoded ps.Z-fil
Level spacings and periodic orbits
Starting from a semiclassical quantization condition based on the trace
formula, we derive a periodic-orbit formula for the distribution of spacings of
eigenvalues with k intermediate levels. Numerical tests verify the validity of
this representation for the nearest-neighbor level spacing (k=0). In a second
part, we present an asymptotic evaluation for large spacings, where consistency
with random matrix theory is achieved for large k. We also discuss the relation
with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for
two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of
validity of asymptotic evaluation clarifie
Whole Farm Modeling of the Effect of Risk on Optimal Tillage and Nitrogen Fertilizer Intensity
nitrogen, tillage, risk, risk aversion, Crop Production/Industries, Farm Management, Production Economics, Risk and Uncertainty,
CMB Anisotropy of Spherical Spaces
The first-year WMAP data taken at their face value hint that the Universe
might be slightly positively curved and therefore necessarily finite, since all
spherical (Clifford-Klein) space forms M^3 = S^3/Gamma, given by the quotient
of S^3 by a group Gamma of covering transformations, possess this property. We
examine the anisotropy of the cosmic microwave background (CMB) for all typical
groups Gamma corresponding to homogeneous universes. The CMB angular power
spectrum and the temperature correlation function are computed for the
homogeneous spaces as a function of the total energy density parameter
Omega_tot in the large range [1.01, 1.20] and are compared with the WMAP data.
We find that out of the infinitely many homogeneous spaces only the three
corresponding to the binary dihedral group T*, the binary octahedral group O*,
and the binary icosahedral group I* are in agreement with the WMAP
observations. Furthermore, if Omega_tot is restricted to the interval [1.00,
1.04], the space described by T* is excluded since it requires a value of
Omega_tot which is probably too large being in the range [1.06, 1.07]. We thus
conclude that there remain only the two homogeneous spherical spaces S^3/O* and
S^3/I* with Omega_tot of about 1.038 and 1.018, respectively, as possible
topologies for our Universe.Comment: A version with high resolution sky maps can be obtained at
http://www.physik.uni-ulm.de/theo/qc
Hot pixel contamination in the CMB correlation function?
Recently, it was suggested that the map-making procedure, which is applied to
the time-ordered CMB data by the WMAP team, might be flawed by hot pixels. This
could lead to a bias in the pixels having an angular distance of about 141
degrees from hot pixels due to the differential measuring process of the
satellite WMAP. Here, the bias is confirmed, and the temperature two-point
correlation function C(theta) is reevaluated by excluding the affected pixels.
It is shown that the most significant effect occurs in C(theta) at the largest
angles near theta = 180 degrees. Furthermore, the corrected correlation
function C(theta) is applied to the cubic topology of the Universe, and it is
found that such a multi-connected universe matches the temperature correlation
better than the LCDM concordance model, provided the cubic length scale is
close to L=4 measured in units of the Hubble length
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