8,446 research outputs found
Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited
The fluctuations exhibited by the cross-sections generated in a
compound-nucleus reaction or, more generally, in a quantum-chaotic scattering
process, when varying the excitation energy or another external parameter, are
characterized by the width Gamma_corr of the cross-section correlation
function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a
method for its determination by simply counting the number of maxima featured
by the cross sections as function of the parameter under consideration. They,
actually, stated that the product of the average number of maxima per unit
energy range and Gamma_corr is constant in the Ercison region of strongly
overlapping resonances. We use the analogy between the scattering formalism for
compound-nucleus reactions and for microwave resonators to test this method
experimentally with unprecedented accuracy using large data sets and propose an
analytical description for the regions of isolated and overlapping resonances
Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard
This article presents experimental results on properties of waves propagating
in an unbounded and a bounded photonic crystal consisting of metallic cylinders
which are arranged in a triangular lattice. First, we present transmission
measurements of plane waves traversing a photonic crystal. The experiments are
performed in the vicinity of a Dirac point, i.e., an isolated conical
singularity of the photonic band structure. There, the transmission shows a
pseudodiffusive 1/L dependence, with being the thickness of the crystal, a
phenomenon also observed in graphene. Second, eigenmode intensity distributions
measured in a microwave analog of a relativistic Dirac billiard, a rectangular
microwave billiard that contains a photonic crystal, are discussed. Close to
the Dirac point states have been detected which are localized at the straight
edge of the photonic crystal corresponding to a zigzag edge in graphene
Static axisymmetric spacetimes with non-generic world-line SUSY
The conditions for the existence of Killing-Yano tensors, which are closely
related to the appearance of non-generic world-line SUSY, are presented for
static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set
of solutions admitting Killing-Yano tensors is considered. In particular, it is
shown that static, axisymmetric and asymptotically flat vacuum solutions
admitting Killing-Yano tensors are only the Schwarzschild solution.Comment: 10 pages (RevTeX), TIT/HEP-253/COSMO-4
Cross-Section Fluctuations in Chaotic Scattering
For the theoretical prediction of cross-section fluctuations in chaotic
scattering, the cross-section autocorrelation function is needed. That function
is not known analytically. Using experimental data and numerical simulations,
we show that an analytical approximation to the cross-section autocorrelation
function can be obtained with the help of expressions first derived by Davis
and Boose. Given the values of the average S-matrix elements and the mean level
density of the scattering system, one can then reliably predict cross-section
fluctuations
Application of a trace formula to the spectra of flat three-dimensional dielectric resonators
The length spectra of flat three-dimensional dielectric resonators of
circular shape were determined from a microwave experiment. They were compared
to a semiclassical trace formula obtained within a two-dimensional model based
on the effective index of refraction approximation and a good agreement was
found. It was necessary to take into account the dispersion of the effective
index of refraction for the two-dimensional approximation. Furthermore, small
deviations between the experimental length spectrum and the trace formula
prediction were attributed to the systematic error of the effective index of
refraction approximation. In summary, the methods developed in this article
enable the application of the trace formula for two-dimensional dielectric
resonators also to realistic, flat three-dimensional dielectric microcavities
and -lasers, allowing for the interpretation of their spectra in terms of
classical periodic orbits.Comment: 13 pages, 12 figures, 1 tabl
Spectral properties of Bunimovich mushroom billiards
Properties of a quantum mushroom billiard in the form of a superconducting
microwave resonator have been investigated. They reveal unexpected nonuniversal
features such as, e.g., a supershell effect in the level density and a dip in
the nearest-neighbor spacing distribution. Theoretical predictions for the
quantum properties of mixed systems rely on the sharp separability of phase
space - an unusual property met by mushroom billiards. We however find
deviations which are ascribed to the presence of dynamic tunneling.Comment: 4 pages, 7 .eps-figure
Correlation Widths in Quantum--Chaotic Scattering
An important parameter to characterize the scattering matrix S for
quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix
autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c
T_c (where d is the mean resonance spacing, T_c with 0 <= T_c <= 1 the
"transmission coefficient" in channel c and where the sum runs over all
channels) provides a very good approximation to Gamma_{corr} even when the
number of channels is small. That same conclusion applies also to the
cross-section correlation function
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