164 research outputs found
Influence of branch points in the complex plane on the transmission through double quantum dots
We consider single-channel transmission through a double quantum dot system
consisting of two single dots that are connected by a wire and coupled each to
one lead. The system is described in the framework of the S-matrix theory by
using the effective Hamiltonian of the open quantum system. It consists of the
Hamiltonian of the closed system (without attached leads) and a term that
accounts for the coupling of the states via the continuum of propagating modes
in the leads. This model allows to study the physical meaning of branch points
in the complex plane. They are points of coalesced eigenvalues and separate the
two scenarios with avoided level crossings and without any crossings in the
complex plane. They influence strongly the features of transmission through
double quantum dots.Comment: 30 pages, 14 figure
Field quantization for chaotic resonators with overlapping modes
Feshbach's projector technique is employed to quantize the electromagnetic
field in optical resonators with an arbitray number of escape channels. We find
spectrally overlapping resonator modes coupled due to the damping and noise
inflicted by the external radiation field. For wave chaotic resonators the mode
dynamics is determined by a non--Hermitean random matrix. Upon including an
amplifying medium, our dynamics of open-resonator modes may serve as a starting
point for a quantum theory of random lasing.Comment: 4 pages, 1 figur
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
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
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
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
A Deeply Virtual Compton Scattering Amplitude
A factorized Regge-pole model for deeply virtual Compton scattering is
suggested. The use of an effective logarithmic Regge-Pomeron trajectory
provides for the description of both ``soft'' (small ) and ``hard'' (large
) dynamics. The model contains explicitly the photoproduction and the DIS
limits and fits the existing HERA data on deeply virtual Compton scattering.Comment: 10 pages, 3 figure
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