2,986 research outputs found
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
Pulsar Magnetospheric Emission Mapping: Images and Implications of Polar-Cap Weather
The beautiful sequences of ``drifting'' subpulses observed in some radio
pulsars have been regarded as among the most salient and potentially
instructive characteristics of their emission, not least because they have
appeared to represent a system of subbeams in motion within the emission zone
of the star. Numerous studies of these ``drift'' sequences have been published,
and a model of their generation and motion articulated long ago by Ruderman &
Sutherland (1975); but efforts thus far have failed to establish an
illuminating connection between the drift phemomenon and the actual sites of
radio emission. Through a detailed analysis of a nearly coherent sequence of
``drifting'' pulses from pulsar B0943+10, we have in fact identified a system
of subbeams circulating around the magnetic axis of the star. A mapping
technique, involving a ``cartographic'' transform and its inverse, permits us
to study the character of the polar-cap emission ``map'' and then to confirm
that it, in turn, represents the observed pulse sequence. On this basis, we
have been able to trace the physical origin of the ``drifting-subpulse''
emission to a stably rotating and remarkably organized configuration of
emission columns, in turn traceable possibly to the magnetic polar-cap ``gap''
region envisioned by some theories.Comment: latex with five eps figure
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
Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs II: semiclassical approach
A semiclassical approach to the universal ergodic spectral statistics in
quantum star graphs is presented for all known ten symmetry classes of quantum
systems. The approach is based on periodic orbit theory, the exact
semiclassical trace formula for star graphs and on diagrammatic techniques. The
appropriate spectral form factors are calculated upto one order beyond the
diagonal and self-dual approximations. The results are in accordance with the
corresponding random-matrix theories which supports a properly generalized
Bohigas-Giannoni-Schmit conjecture.Comment: 15 Page
On the Accuracy of the Semiclassical Trace Formula
The semiclassical trace formula provides the basic construction from which
one derives the semiclassical approximation for the spectrum of quantum systems
which are chaotic in the classical limit. When the dimensionality of the system
increases, the mean level spacing decreases as , while the
semiclassical approximation is commonly believed to provide an accuracy of
order , independently of d. If this were true, the semiclassical trace
formula would be limited to systems in d <= 2 only. In the present work we set
about to define proper measures of the semiclassical spectral accuracy, and to
propose theoretical and numerical evidence to the effect that the semiclassical
accuracy, measured in units of the mean level spacing, depends only weakly (if
at all) on the dimensionality. Detailed and thorough numerical tests were
performed for the Sinai billiard in 2 and 3 dimensions, substantiating the
theoretical arguments.Comment: LaTeX, 31 pages, 14 figures, final version (minor changes
Geometrical theory of diffraction and spectral statistics
We investigate the influence of diffraction on the statistics of energy
levels in quantum systems with a chaotic classical limit. By applying the
geometrical theory of diffraction we show that diffraction on singularities of
the potential can lead to modifications in semiclassical approximations for
spectral statistics that persist in the semiclassical limit . This
result is obtained by deriving a classical sum rule for trajectories that
connect two points in coordinate space.Comment: 14 pages, no figure, to appear in J. Phys.
Periodic-Orbit Bifurcations and Superdeformed Shell Structure
We have derived a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences occurring at
bifurcations and in the spherical limit, the trace integrals over the
action-angle variables were performed using an improved stationary phase
method. The resulting semiclassical level density oscillations and
shell-correction energies are in good agreement with quantum-mechanical
results. We find that the bifurcations of some dominant short periodic orbits
lead to an enhancement of the shell structure for "superdeformed" shapes
related to those known from atomic nuclei.Comment: 4 pages including 3 figure
Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
We present a quantitative semiclassical treatment of the effects of
bifurcations on the spectral rigidity and the spectral form factor of a
Hamiltonian quantum system defined by two coupled quartic oscillators, which on
the classical level exhibits mixed phase space dynamics. We show that the
signature of a pitchfork bifurcation is two-fold: Beside the known effect of an
enhanced periodic orbit contribution due to its peculiar -dependence at
the bifurcation, we demonstrate that the orbit pair born {\em at} the
bifurcation gives rise to distinct deviations from universality slightly {\em
above} the bifurcation. This requires a semiclassical treatment beyond the
so-called diagonal approximation. Our semiclassical predictions for both the
coarse-grained density of states and the spectral rigidity, are in excellent
agreement with corresponding quantum-mechanical results.Comment: LaTex, 25 pp., 14 Figures (26 *.eps files); final version 3, to be
published in Journal of Physics
Nonperiodic Orbit Sums in Weyl's Expansion for Billiards
Weyl's expansion for the asymptotic mode density of billiards consists of the
area, length, curvature and corner terms. The area term has been associated
with the so-called zero-length orbits. Here closed nonperiodic paths
corresponding to the length and corner terms are constructed.Comment: 8 pages, 2 figure
Form factor for large quantum graphs: evaluating orbits with time-reversal
It has been shown that for a certain special type of quantum graphs the
random-matrix form factor can be recovered to at least third order in the
scaled time \tau using periodic-orbit theory. Two types of contributing pairs
of orbits were identified, those which require time-reversal symmetry and those
which do not. We present a new technique of dealing with contribution from the
former type of orbits.
The technique allows us to derive the third order term of the expansion for
general graphs. Although the derivation is rather technical, the advantages of
the technique are obvious: it makes the derivation tractable, it identifies
explicitly the orbit configurations which give the correct contribution, it is
more algorithmical and more system-independent, making possible future
applications of the technique to systems other than quantum graphs.Comment: 25 pages, 14 figures, accepted to Waves in Random Media (special
issue on Quantum Graphs and their Applications). Fixed typos, removed an
overly restrictive condition (appendix), shortened introductory section
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