16 research outputs found
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.
Bound states in the continuum in open Aharonov-Bohm rings
Using formalism of effective Hamiltonian we consider bound states in
continuum (BIC). They are those eigen states of non-hermitian effective
Hamiltonian which have real eigen values. It is shown that BICs are orthogonal
to open channels of the leads, i.e. disconnected from the continuum. As a
result BICs can be superposed to transport solution with arbitrary coefficient
and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are
opened by attaching single-channel leads to them allow exact consideration of
BICs. BICs occur at discrete values of energy and magnetic flux however it's
realization strongly depend on a way to the BIC's point.Comment: 5 pgaes, 4 figure
Phase transitions in open quantum systems
We consider the behaviour of open quantum systems in dependence on the
coupling to one decay channel by introducing the coupling parameter
being proportional to the average degree of overlapping. Under critical
conditions, a reorganization of the spectrum takes place which creates a
bifurcation of the time scales with respect to the lifetimes of the resonance
states. We derive analytically the conditions under which the reorganization
process can be understood as a second-order phase transition and illustrate our
results by numerical investigations. The conditions are fulfilled e.g. for a
picket fence with equal coupling of the states to the continuum. Energy
dependencies within the system are included. We consider also the generic case
of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the
reorganization of the spectrum occurs at the critical value of
the control parameter globally over the whole energy range of the spectrum. All
states act cooperatively.Comment: 28 pages, 22 Postscript figure
Random Matrix Theories in Quantum Physics: Common Concepts
We review the development of random-matrix theory (RMT) during the last
decade. We emphasize both the theoretical aspects, and the application of the
theory to a number of fields. These comprise chaotic and disordered systems,
the localization problem, many-body quantum systems, the Calogero-Sutherland
model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions.
The review is preceded by a brief historical survey of the developments of RMT
and of localization theory since their inception. We emphasize the concepts
common to the above-mentioned fields as well as the great diversity of RMT. In
view of the universality of RMT, we suggest that the current development
signals the emergence of a new "statistical mechanics": Stochasticity and
general symmetry requirements lead to universal laws not based on dynamical
principles.Comment: 178 pages, Revtex, 45 figures, submitted to Physics Report