10 research outputs found
Correlation functions of impedance and scattering matrix elements in chaotic absorbing cavities
Wave scattering in chaotic systems with a uniform energy loss (absorption) is
considered. Within the random matrix approach we calculate exactly the energy
correlation functions of different matrix elements of impedance or scattering
matrices for systems with preserved or broken time-reversal symmetry. The
obtained results are valid at any number of arbitrary open scattering channels
and arbitrary absorption. Elastic enhancement factors (defined through the
ratio of the corresponding variance in reflection to that in transmission) are
also discussed.Comment: 10 pages, 2 figures (misprints corrected and references updated in
ver.2); to appear in Acta Phys. Pol. A (Proceedings of the 2nd Workshop on
Quantum Chaos and Localization Phenomena, May 19-22, 2005, Warsaw
Random matrix description of decaying quantum systems
This contribution describes a statistical model for decaying quantum systems
(e.g. photo-dissociation or -ionization). It takes the interference between
direct and indirect decay processes explicitely into account. The resulting
expressions for the partial decay amplitudes and the corresponding cross
sections may be considered a many-channel many-resonance generalization of
Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)].
A statistical (random matrix) model is then introduced. It allows to describe
chaotic scattering systems with tunable couplings to the decay channels. We
focus on the autocorrelation function of the total (photo) cross section, and
we find that it depends on the same combination of parameters, as the
Fano-parameter distribution. These combinations are statistical variants of the
one-channel Fano parameter. It is thus possible to study Fano interference
(i.e. the interference between direct and indirect decay paths) on the basis of
the autocorrelation function, and thereby in the regime of overlapping
resonances. It allows us, to study the Fano interference in the limit of
strongly overlapping resonances, where we find a persisting effect on the level
of the weak localization correction.Comment: 16 pages, 2 figure
Random Matrices close to Hermitian or unitary: overview of methods and results
The paper discusses progress in understanding statistical properties of
complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and
non-Hermitian random matrices. Ensembles of this type emerge in various
physical contexts, most importantly in random matrix description of quantum
chaotic scattering as well as in the context of QCD-inspired random matrix
models.Comment: Published version, with a few more misprints correcte
Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
We review recent developments on quantum scattering from mesoscopic systems.
Various spatial geometries whose closed analogs shows diffusive, localized or
critical behavior are considered. These are features that cannot be described
by the universal Random Matrix Theory results. Instead one has to go beyond
this approximation and incorporate them in a non-perturbative way. Here, we pay
particular emphasis to the traces of these non-universal characteristics, in
the distribution of the Wigner delay times and resonance widths. The former
quantity captures time dependent aspects of quantum scattering while the latter
is associated with the poles of the scattering matrix.Comment: 30 pages, 15 figures (submitted to Journal of Phys. A: Math. and
General, special issue on "Aspects of Quantum Chaotic Scattering"
Charge fluctuations in open chaotic cavities
We present a discussion of the charge response and the charge fluctuations of
mesoscopic chaotic cavities in terms of a generalized Wigner-Smith matrix. The
Wigner-Smith matrix is well known in investigations of time-delay of quantum
scattering. It is expressed in terms of the scattering matrix and its
derivatives with energy. We consider a similar matrix but instead of an energy
derivative we investigate the derivative with regard to the electric potential.
The resulting matrix is then the operator of charge. If this charge operator is
combined with a self-consistent treatment of Coulomb interaction, the charge
operator determines the capacitance of the system, the non-dissipative
ac-linear response, the RC-time with a novel charge relaxation resistance, and
in the presence of transport a resistance that governs the displacement
currents induced into a nearby conductor. In particular these capacitances and
resistances determine the relaxation rate and dephasing rate of a nearby qubit
(a double quantum dot). We discuss the role of screening of mesoscopic chaotic
detectors. Coulomb interaction effects in quantum pumping and in photon
assisted electron-hole shot noise are treated similarly. For the latter we
present novel results for chaotic cavities with non-ideal leads.Comment: 29 pages, 13 figures;v.2--minor changes; contribution for the special
issue of J. Phys. A on "Trends in Quantum Chaotic Scattering
Classical wave experiments on chaotic scattering
We review recent research on the transport properties of classical waves
through chaotic systems with special emphasis on microwaves and sound waves.
Inasmuch as these experiments use antennas or transducers to couple waves into
or out of the systems, scattering theory has to be applied for a quantitative
interpretation of the measurements. Most experiments concentrate on tests of
predictions from random matrix theory and the random plane wave approximation.
In all studied examples a quantitative agreement between experiment and theory
is achieved. To this end it is necessary, however, to take absorption and
imperfect coupling into account, concepts that were ignored in most previous
theoretical investigations. Classical phase space signatures of scattering are
being examined in a small number of experiments.Comment: 33 pages, 13 figures; invited review for the Special Issue of J.
Phys. A: Math. Gen. on "Trends in Quantum Chaotic Scattering