156 research outputs found
Spectroscopic studies in open quantum systems
The spectroscopic properties of an open quantum system are determined by the
eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the
Hamiltonian H_0 of the corresponding closed system and a non-Hermitian
correction term W arising from the interaction via the continuum of decay
channels. The eigenvalues E_R of H are complex. They are the poles of the
S-matrix and provide both the energies and widths of the states. We illustrate
the interplay between Re(H) and Im(H) by means of the different interference
phenomena between two neighboured resonance states. Level repulsion along the
real axis appears if the interaction is caused mainly by Re(H) while a
bifurcation of the widths appears if the interaction occurs mainly due to
Im(H). We then calculate the poles of the S-matrix and the corresponding
wavefunctions for a rectangular microwave resonator with a scatter as a
function of the area of the resonator as well as of the degree of opening to a
guide. The calculations are performed by using the method of exterior complex
scaling. Re(W) and Im(W) cause changes in the structure of the wavefunctions
which are permanent, as a rule. At full opening to the lead, short-lived
collective states are formed together with long-lived trapped states. The
wavefunctions of the short-lived states at full opening to the lead are very
different from those at small opening. The resonance picture obtained from the
microwave resonator shows all the characteristic features known from the study
of many-body systems in spite of the absence of two-body forces. The poles of
the S-matrix determine the conductance of the resonator. Effects arising from
the interplay between resonance trapping and level repulsion along the real
axis are not involved in the statistical theory.Comment: The six jpg files are not included in the tex-fil
Four-Parameter Point-Interaction in 1-D Quantum Systems
We construct a four-parameter point-interaction for a non-relativistic
particle moving on a line as the limit of a short range interaction with range
tending toward zero. For particular choices of the parameters, we can obtain a
delta-interaction or the so-called delta'-interaction. The Hamiltonian
corresponding to the four-parameter point-interaction is shown to correspond to
the four-parameter self-adjoint Hamiltonian of the free particle moving on the
line with the origin excluded.Comment: 6 pages, Plain Tex file. BU-HEP-92-
Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling
The distributions of inter-island gaps and captures zones for islands
nucleated on a one-dimensional substrate during submonolayer deposition are
considered using a novel retrospective view. This provides an alternative
perspective on why scaling occurs in this continuously evolving system.
Distributional fixed point equations for the gaps are derived both with and
without a mean field approximation for nearest neighbour gap size correlation.
Solutions to the equations show that correct consideration of fragmentation
bias justifies the mean field approach which can be extended to provide
closed-from equations for the capture zones. Our results compare favourably to
Monte Carlo data for both point and extended islands using a range of critical
island size . We also find satisfactory agreement with theoretical
models based on more traditional fragmentation theory approaches.Comment: 9 pages, 7 figures and 1 tabl
Spread Spectrum Watermarking: Principles and Applications in Fading Channel
ISBN 978-953-51-0618-
Resonance statistics in a microwave cavity with a thin antenna
We propose a model for scattering in a flat resonator with a thin antenna.
The results are applied to rectangular microwave cavities. We compute the
resonance spacing distribution and show that it agrees well with experimental
data provided the antenna radius is much smaller than wavelengths of the
resonance wavefunctions.Comment: 10 pages LaTeX source file with one ps figure; to appear in
Phys.Lett.
The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles
We analyze statistical properties of the city bus transport in Cuernavaca
(Mexico) and show that the bus arrivals display probability distributions
conforming those given by the Unitary Ensemble of random matrices.Comment: 4 pages, 3 figure
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