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 $i=0,1,2,3$. 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