5,875 research outputs found
Power-law random banded matrices and ultrametric matrices: eigenvector distribution in the intermediate regime
The power-law random banded matrices and the ultrametric random matrices are
investigated numerically in the regime where eigenstates are extended but all
integer matrix moments remain finite in the limit of large matrix dimensions.
Though in this case standard analytical tools are inapplicable, we found that
in all considered cases eigenvector distributions are extremely well described
by the generalised hyperbolic distribution which differs considerably from the
usual Porter-Thomas distribution but shares with it certain universal
properties.Comment: 20 pages, 12 figure
Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics
We discuss the localization of wavefunctions along planes containing the
shortest periodic orbits in a three-dimensional billiard system with axial
symmetry. This model mimicks the self-consistent mean field of a heavy nucleus
at deformations that occur characteristically during the fission process [1,2].
Many actinide nuclei become unstable against left-right asymmetric
deformations, which results in asymmetric fragment mass distributions. Recently
we have shown [3,4] that the onset of this asymmetry can be explained in the
semiclassical periodic orbit theory by a few short periodic orbits lying in
planes perpendicular to the symmetry axis. Presently we show that these orbits
are surrounded by small islands of stability in an otherwise chaotic phase
space, and that the wavefunctions of the diabatic quantum states that are most
sensitive to the left-right asymmetry have their extrema in the same planes. An
EBK quantization of the classical motion near these planes reproduces the exact
eigenenergies of the diabatic quantum states surprisingly well.Comment: 4 pages, 5 figures, contribution to the Nobel Symposium on Quantum
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Semiclassical Theory of Chaotic Quantum Transport
We present a refined semiclassical approach to the Landauer conductance and
Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for
systems with uniformly hyperbolic dynamics that including off-diagonal
contributions to double sums over classical paths gives a weak-localization
correction in quantitative agreement with results from random matrix theory. We
further discuss the magnetic field dependence. This semiclassical treatment
accounts for current conservation.Comment: 4 pages, 1 figur
Trace formula for a dielectric microdisk with a point scatterer
Two-dimensional dielectric microcavities are of widespread use in microoptics
applications. Recently, a trace formula has been established for dielectric
cavities which relates their resonance spectrum to the periodic rays inside the
cavity. In the present paper we extend this trace formula to a dielectric disk
with a small scatterer. This system has been introduced for microlaser
applications, because it has long-lived resonances with strongly directional
far field. We show that its resonance spectrum contains signatures not only of
periodic rays, but also of diffractive rays that occur in Keller's geometrical
theory of diffraction. We compare our results with those for a closed cavity
with Dirichlet boundary conditions.Comment: 39 pages, 18 figures, pdflate
Microdisk Resonators with Two Point Scatterers
Optical microdisk resonators exhibit modes with extremely high Q-factors. Their low lasing thresholds make circular microresonators good candidates for the realization of miniature laser sources. They have, however, the serious drawback that their light emission is isotropic, which is inconvenient for many applications. In our previous work, we showed that the presence of a point scatterer inside the disk can lead to highly directional modes in various frequency ranges while preserving the high Q-factors. In the present paper we generalize this idea to two point scatterers. The motivation for this work is that the strength of a point scatterer is difficult to control in experiments, and the presence of a second scatterer leads to a higher dimensional parameter space which permits to compensate this deficiency. Similar to the case of a single scatterer in a circular disk, the problem of finding the resonance modes in the presence of two scatterers is to a large extent analytically tractable.
Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs
Physicists have argued that periodic orbit bunching leads to universal
spectral fluctuations for chaotic quantum systems. To establish a more detailed
mathematical understanding of this fact, it is first necessary to look more
closely at the classical side of the problem and determine orbit pairs
consisting of orbits which have similar actions. In this paper we specialize to
the geodesic flow on compact factors of the hyperbolic plane as a classical
chaotic system. We prove the existence of a periodic partner orbit for a given
periodic orbit which has a small-angle self-crossing in configuration space
which is a `2-encounter'; such configurations are called `Sieber-Richter pairs'
in the physics literature. Furthermore, we derive an estimate for the action
difference of the partners. In the second part of this paper [13], an inductive
argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit
Radio observations of four anticenter 2CG gamma-ray sources
The 2CG sources 218-00, 135+01, 121+04 and 95+04 have been observed at two radio frequencies and the flux values and spectra of the radio sources observed within the gamma-ray fields are catalogued down to a sensitivity of approx 30 mJy at lambda 11 cm. Possible gamma-ray counterpart candidate objects are briefly discussed
Spectral statistics in chaotic systems with a point interaction
We consider quantum systems with a chaotic classical limit that are perturbed
by a point-like scatterer. The spectral form factor K(tau) for these systems is
evaluated semiclassically in terms of periodic and diffractive orbits. It is
shown for order tau^2 and tau^3 that off-diagonal contributions to the form
factor which involve diffractive orbits cancel exactly the diagonal
contributions from diffractive orbits, implying that the perturbation by the
scatterer does not change the spectral statistic. We further show that
parametric spectral statistics for these systems are universal for small
changes of the strength of the scatterer.Comment: LaTeX, 21 pages, 7 figures, small corrections, new references adde
Internal and External Resonances of Dielectric Disks
Circular microresonators (microdisks) are micron sized dielectric disks
embedded in a material of lower refractive index. They possess modes with
complex eigenvalues (resonances) which are solutions of analytically given
transcendental equations. The behavior of such eigenvalues in the small opening
limit, i.e. when the refractive index of the cavity goes to infinity, is
analysed. This analysis allows one to clearly distinguish between internal
(Feshbach) and external (shape) resonant modes for both TM and TE
polarizations. This is especially important for TE polarization for which
internal and external resonances can be found in the same region of the complex
wavenumber plane. It is also shown that for both polarizations, the internal as
well as external resonances can be classified by well defined azimuthal and
radial modal indices.Comment: 5 pages, 8 figures, pdflate
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