122 research outputs found
Effective Coupling for Open Billiards
We derive an explicit expression for the coupling constants of individual
eigenstates of a closed billiard which is opened by attaching a waveguide. The
Wigner time delay and the resonance positions resulting from the coupling
constants are compared to an exact numerical calculation. Deviations can be
attributed to evanescent modes in the waveguide and to the finite number of
eigenstates taken into account. The influence of the shape of the billiard and
of the boundary conditions at the mouth of the waveguide are also discussed.
Finally we show that the mean value of the dimensionless coupling constants
tends to the critical value when the eigenstates of the billiard follow
random-matrix theory
The Rarita--Schwinger field: renormalization and phenomenology
We discuss renormalization of propagator of interacting Rarita--Schwinger
field. Spin-3/2 contribution after renormalization takes usual resonance form.
For non-leading spin-1/2 terms we found procedure, which guarantees absence of
poles in energy plane. The obtained renormalized propagator has one free
parameter and is a straight generalization of the famous free propagator of
Moldauer and Case. Application of this propagator for production of
in \pi^{+}\particle{p}\to \pi^{+}\particle{p} leads to
good description of total cross-section and to reasonable agreement with
results of partial wave analysis.Comment: 19 pages, 3 figures, revtex4; misprints, min editorial change
Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances
We derive the explicit expression for the distribution of resonance widths in
a chaotic quantum system coupled to continua via M equivalent open channels. It
describes a crossover from the distribution (regime of isolated
resonances) to a broad power-like distribution typical for the regime of
overlapping resonances. The first moment is found to reproduce exactly the
Moldauer-Simonius relation between the mean resonance width and the
transmission coefficient. This fact may serve as another manifestation of
equivalence between the spectral and the ensemble averaging.Comment: 4 two-column pages, RevTex. text is slightly modified; some misprints
are correcte
Quantum Graphs: A simple model for Chaotic Scattering
We connect quantum graphs with infinite leads, and turn them to scattering
systems. We show that they display all the features which characterize quantum
scattering systems with an underlying classical chaotic dynamics: typical
poles, delay time and conductance distributions, Ericson fluctuations, and when
considered statistically, the ensemble of scattering matrices reproduce quite
well the predictions of appropriately defined Random Matrix ensembles. The
underlying classical dynamics can be defined, and it provides important
parameters which are needed for the quantum theory. In particular, we derive
exact expressions for the scattering matrix, and an exact trace formula for the
density of resonances, in terms of classical orbits, analogous to the
semiclassical theory of chaotic scattering. We use this in order to investigate
the origin of the connection between Random Matrix Theory and the underlying
classical chaotic dynamics. Being an exact theory, and due to its relative
simplicity, it offers new insights into this problem which is at the fore-front
of the research in chaotic scattering and related fields.Comment: 28 pages, 13 figures, submitted to J. Phys. A Special Issue -- Random
Matrix Theor
Multiscale fluctuations in nuclear response
The nuclear collective response is investigated in the framework of a doorway
picture in which the spreading width of the collective motion is described as a
coupling to more and more complex configurations. It is shown that this
coupling induces fluctuations of the observed strength. In the case of a
hierarchy of overlapping decay channels, we observe Ericson fluctuations at
different scales. Methods for extracting these scales and the related lifetimes
are discussed. Finally, we show that the coupling of different states at one
level of complexity to some common decay channels at the next level, may
produce interference-like patterns in the nuclear response. This quantum effect
leads to a new type of fluctuations with a typical width related to the level
spacing.Comment: 34 Latex pages including 6 figures (submitted to Phys. Rev. C
Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths
A phenomenological schematic model of multipole giant resonances (GR) is
considered which treats the external interaction via common decay channels on
the same footing as the coherent part of the internal residual interaction. The
damping due to the coupling to the sea of complicated states is neglected. As a
result, the formation of GR is governed by the interplay and competition of two
kinds of collectivity, the internal and the external one. The mixing of the
doorway components of a GR due to the external interaction influences
significantly their multipole strengths, widths and positions in energy. In
particular, a narrow resonance state with an appreciable multipole strength is
formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997
Observation of resonance trapping in an open microwave cavity
The coupling of a quantum mechanical system to open decay channels has been
theoretically studied in numerous works, mainly in the context of nuclear
physics but also in atomic, molecular and mesoscopic physics. Theory predicts
that with increasing coupling strength to the channels the resonance widths of
all states should first increase but finally decrease again for most of the
states. In this letter, the first direct experimental verification of this
effect, known as resonance trapping, is presented. In the experiment a
microwave Sinai cavity with an attached waveguide with variable slit width was
used.Comment: to be published in Phys. Rev. Let
Resonance trapping and saturation of decay widths
Resonance trapping appears in open many-particle quantum systems at high
level density when the coupling to the continuum of decay channels reaches a
critical strength. Here a reorganization of the system takes place and a
separation of different time scales appears. We investigate it under the
influence of additional weakly coupled channels as well as by taking into
account the real part of the coupling term between system and continuum. We
observe a saturation of the mean width of the trapped states. Also the decay
rates saturate as a function of the coupling strength. The mechanism of the
saturation is studied in detail. In any case, the critical region of
reorganization is enlarged. When the transmission coefficients for the
different channels are different, the width distribution is broadened as
compared to a chi_K^2 distribution where K is the number of channels. Resonance
trapping takes place before the broad state overlaps regions beyond the
extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.
Effective Lagrangian Approach to the Theory of Eta Photoproduction in the Region
We investigate eta photoproduction in the resonance region
within the effective Lagrangian approach (ELA), wherein leading contributions
to the amplitude at the tree level are taken into account. These include the
nucleon Born terms and the leading -channel vector meson exchanges as the
non-resonant pieces. In addition, we consider five resonance contributions in
the - and - channel; besides the dominant , these are:
and . The amplitudes for the
and the photoproduction near threshold have significant
differences, even as they share common contributions, such as those of the
nucleon Born terms. Among these differences, the contribution to the
photoproduction of the -channel excitation of the is the most
significant. We find the off-shell properties of the spin-3/2 resonances to be
important in determining the background contributions. Fitting our effective
amplitude to the available data base allows us to extract the quantity
, characteristic of the
photoexcitation of the resonance and its decay into the
-nucleon channel, of interest to precise tests of hadron models. At the
photon point, we determine it to be from
the old data base, and from a
combination of old data base and new Bates data. We obtain the helicity
amplitude for to be from the old data base, and from the combination of the old data base and new Bates
data, compared with the results of the analysis of pion photoproduction
yielding , in the same units.Comment: 43 pages, RevTeX, 9 figures available upon request, to appear in
Phys. Rev.
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