22,879 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
Integrability and Disorder in Mesoscopic Systems: Application to Orbital Magnetism
We present a semiclassical theory of weak disorder effects in small
structures and apply it to the magnetic response of non-interacting electrons
confined in integrable geometries. We discuss the various averaging procedures
describing different experimental situations in terms of one- and two-particle
Green functions. We demonstrate that the anomalously large zero-field
susceptibility characteristic of clean integrable structures is only weakly
suppressed by disorder. This damping depends on the ratio of the typical size
of the structure with the two characteristic length scales describing the
disorder (elastic mean-free-path and correlation length of the potential) in a
power-law form for the experimentally relevant parameter region. We establish
the comparison with the available experimental data and we extend the study of
the interplay between disorder and integrability to finite magnetic fields.Comment: 38 pages, Latex, 7 Postscript figures, 1 table, to appear in Jour.
Math. Physics 199
Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards
Using reciprocity, we investigate the breaking of time-reversal (T) symmetry
due to a ferrite embedded in a flat microwave billiard. Transmission spectra of
isolated single resonances are not sensitive to T-violation whereas those of
pairs of nearly degenerate resonances do depend on the direction of time. For
their theoretical description a scattering matrix model from nuclear physics is
used. The T-violating matrix elements of the effective Hamiltonian for the
microwave billiard with the embedded ferrite are determined experimentally as
functions of the magnetization of the ferrite.Comment: 4 pages, 4 figure
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
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
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
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