138 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.
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
Trace identities and their semiclassical implications
The compatibility of the semiclassical quantization of area-preserving maps
with some exact identities which follow from the unitarity of the quantum
evolution operator is discussed. The quantum identities involve relations
between traces of powers of the evolution operator. For classically {\it
integrable} maps, the semiclassical approximation is shown to be compatible
with the trace identities. This is done by the identification of stationary
phase manifolds which give the main contributions to the result. The same
technique is not applicable for {\it chaotic} maps, and the compatibility of
the semiclassical theory in this case remains unsettled. The compatibility of
the semiclassical quantization with the trace identities demonstrates the
crucial importance of non-diagonal contributions.Comment: LaTeX - IOP styl
Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems
Phase transitions in open quantum systems, which are associated with the
formation of collective states of a large width and of trapped states with
rather small widths, are related to exceptional points of the Hamiltonian.
Exceptional points are the singularities of the spectrum and eigenfunctions,
when they are considered as functions of a coupling parameter. In the present
paper this parameter is the coupling strength to the continuum. It is shown
that the positions of the exceptional points (their accumulation point in the
thermodynamical limit) depend on the particular type and energy dependence of
the coupling to the continuum in the same way as the transition point of the
corresponding phase transition.Comment: 22 pages, 4 figure
Shape of Pion Distribution Amplitude
A scenario is investigated in which the leading-twist pion distribution
amplitude phi_pi (x) is approximated by the pion decay constant f_pi for all
essential values of the light-cone fraction x. A model for the light-front wave
function Psi(x,k_perp) is proposed that produces such a distribution amplitude
and has a rapidly decreasing (exponential for definiteness) dependence on the
light-front energy combination k_perp^2/x(1-x). It is shown that this model
easily reproduces the fit of recent large-Q^2 BaBar data on the photon-pion
transition form factor. Some aspects of scenario with flat pion distribution
amplitude are discussed.Comment: References added, typos fixed, one figure added, some minor changes
in tex
Signatures of the correlation hole in total and partial cross sections
In a complex scattering system with few open channels, say a quantum dot with
leads, the correlation properties of the poles of the scattering matrix are
most directly related to the internal dynamics of the system. We may ask how to
extract these properties from an analysis of cross sections. In general this is
very difficult, if we leave the domain of isolated resonances. We propose to
consider the cross correlation function of two different elastic or total cross
sections. For these we can show numerically and to some extent also
analytically a significant dependence on the correlations between the
scattering poles. The difference between uncorrelated and strongly correlated
poles is clearly visible, even for strongly overlapping resonances.Comment: 25 pages, 13 Postscript figures, typos corrected and references adde
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
Dynamics of quantum systems
A relation between the eigenvalues of an effective Hamilton operator and the
poles of the matrix is derived which holds for isolated as well as for
overlapping resonance states. The system may be a many-particle quantum system
with two-body forces between the constituents or it may be a quantum billiard
without any two-body forces. Avoided crossings of discrete states as well as of
resonance states are traced back to the existence of branch points in the
complex plane. Under certain conditions, these branch points appear as double
poles of the matrix. They influence the dynamics of open as well as of
closed quantum systems. The dynamics of the two-level system is studied in
detail analytically as well as numerically.Comment: 21 pages 7 figure
The classical limit for a class of quantum baker's maps
We show that the class of quantum baker's maps defined by Schack and Caves
have the proper classical limit provided the number of momentum bits approaches
infinity. This is done by deriving a semi-classical approximation to the
coherent-state propagator.Comment: 18 pages, 5 figure
Optimization by thermal cycling
Thermal cycling is an heuristic optimization algorithm which consists of
cyclically heating and quenching by Metropolis and local search procedures,
respectively, where the amplitude slowly decreases. In recent years, it has
been successfully applied to two combinatorial optimization tasks, the
traveling salesman problem and the search for low-energy states of the Coulomb
glass. In these cases, the algorithm is far more efficient than usual simulated
annealing. In its original form the algorithm was designed only for the case of
discrete variables. Its basic ideas are applicable also to a problem with
continuous variables, the search for low-energy states of Lennard-Jones
clusters.Comment: Submitted to Proceedings of the Workshop "Complexity, Metastability
and Nonextensivity", held in Erice 20-26 July 2004. Latex, 7 pages, 3 figure
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