7,620 research outputs found
Spectral properties of microwave graphs with local absorption
The influence of absorption on the spectra of microwave graphs has been
studied experimentally. The microwave networks were made up of coaxial cables
and T junctions. First, absorption was introduced by attaching a 50 Ohm load to
an additional vertex for graphs with and without time-reversal symmetry. The
resulting level-spacing distributions were compared with a generalization of
the Wigner surmise in the presence of open channels proposed recently by Poli
et al. [Phys. Rev. Lett. 108, 174101 (2012)]. Good agreement was found using an
effective coupling parameter. Second, absorption was introduced along one
individual bond via a variable microwave attenuator, and the influence of
absorption on the length spectrum was studied. The peak heights in the length
spectra corresponding to orbits avoiding the absorber were found to be
independent of the attenuation, whereas, the heights of the peaks belonging to
orbits passing the absorber once or twice showed the expected decrease with
increasing attenuation.Comment: 7 pages, 7 figure
Scaling behavior of a one-dimensional correlated disordered electronic System
A one-dimensional diagonal tight binding electronic system with correlated
disorder is investigated. The correlation of the random potential is
exponentially decaying with distance and its correlation length diverges as the
concentration of "wrong sign" approaches to 1 or 0. The correlated random
number sequence can be generated easily with a binary sequence similar to that
of a one-dimensional spin glass system. The localization length (LL) and the
integrated density of states (IDOS) for long chains are computed. A comparison
with numerical results is made with the recently developed scaling technique
results. The Coherent Potential Approximation (CPA) is also adopted to obtain
scaling functions for both the LL and the IDOS. We confirmed that the scaling
functions show a crossover near the band edge and establish their relation to
the concentration. For concentrations near to 0 or 1 (longer correlation length
case), the scaling behavior is followed only for a very limited range of the
potential strengths.Comment: will appear in PR
Formation and interaction of resonance chains in the open 3-disk system
In ballistic open quantum systems one often observes that the resonances in
the complex-energy plane form a clear chain structure. Taking the open 3-disk
system as a paradigmatic model system, we investigate how this chain structure
is reflected in the resonance states and how it is connected to the underlying
classical dynamics. Using an efficient scattering approach we observe that
resonance states along one chain are clearly correlated while resonance states
of different chains show an anticorrelation. Studying the phase space
representations of the resonance states we find that their localization in
phase space oscillate between different regions of the classical trapped set as
one moves along the chains and that these oscillations are connected to a
modulation of the resonance spacing. A single resonance chain is thus no WKB
quantization of a single periodic orbits, but the structure of several
oscillating chains arises from the interaction of several periodic orbits. We
illuminate the physical mechanism behind these findings by combining the
semiclassical cycle expansion with a quantum graph model.Comment: 25 pages, 15 figure
Experimental Observation of a Fundamental Length Scale of Waves in Random Media
Waves propagating through a weakly scattering random medium show a pronounced
branching of the flow accompanied by the formation of freak waves, i.e.,
extremely intense waves. Theory predicts that this strong fluctuation regime is
accompanied by its own fundamental length scale of transport in random media,
parametrically different from the mean free path or the localization length. We
show numerically how the scintillation index can be used to assess the scaling
behavior of the branching length. We report the experimental observation of
this scaling using microwave transport experiments in quasi-two-dimensional
resonators with randomly distributed weak scatterers. Remarkably, the scaling
range extends much further than expected from random caustics statistics.Comment: 5 pages, 5 figure
A Proposal to Cap Tort Liability: Avoiding the Pitfalls of Heightened Rationality
This Note sets forth a model statute that limits high damage awards, yet will withstand the rigors of judicial scrutiny. After presenting a brief background of the medical malpractice crisis in Part I, Part II outlines the standards of equal protection review that the courts are presently using. The Note then focuses on the constitutional challenges to caps on medical malpractice liability in Part III. Part IV discusses the values and interests that were found to be dispositive in the courts\u27 decisions. Finally, after analyzing the criteria that must be met to ensure that a legislative limitation will survive judicial scrutiny, Part V proposes a statute to circumscribe noneconomic damage awards
Experimental Observation of the Spectral Gap in Microwave n-Disk Systems
Symmetry reduced three-disk and five-disk systems are studied in a microwave
setup. Using harmonic inversion the distribution of the imaginary parts of the
resonances is determined. With increasing opening of the systems, a spectral
gap is observed for thick as well as for thin repellers and for the latter case
it is compared with the known topological pressure bounds. The maxima of the
distributions are found to coincide for a large range of the distance to radius
parameter with half of the classical escape rate. This confirms theoretical
predictions based on rigorous mathematical analysis for the spectral gap and on
numerical experiments for the maxima of the distributions.Comment: 5 pages, 4 figure
First experimental realization of the Dirac oscillator
We present the first experimental microwave realization of the
one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic
systems. The experiment relies on a relation of the Dirac oscillator to a
corresponding tight-binding system. This tight-binding system is implemented as
a microwave system by a chain of coupled dielectric disks, where the coupling
is evanescent and can be adjusted appropriately. The resonances of the finite
microwave system yields the spectrum of the one-dimensional Dirac oscillator
with and without mass term. The flexibility of the experimental set-up allows
the implementation of other one-dimensional Dirac type equations.Comment: 6 figures, 5 page
Dynamical tunneling in mushroom billiards
We study the fundamental question of dynamical tunneling in generic
two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling
rates. Experimentally, we use microwave spectra to investigate a mushroom
billiard with adjustable foot height. Numerically, we obtain tunneling rates
from high precision eigenvalues using the improved method of particular
solutions. Analytically, a prediction is given by extending an approach using a
fictitious integrable system to billiards. In contrast to previous approaches
for billiards, we find agreement with experimental and numerical data without
any free parameter.Comment: 4 pages, 4 figure
On the theory of cavities with point-like perturbations. Part II: Rectangular cavities
We consider an application of a general theory for cavities with point-like
perturbations for a rectangular shape. Hereby we concentrate on experimental
wave patterns obtained for nearly degenerate states. The nodal lines in these
patterns may be broken, which is an effect coming only from the experimental
determination of the patterns. These findings are explained within a framework
of the developed theory.Comment: 14 pages, 3 figure
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