227 research outputs found
Algebraic fidelity decay for local perturbations
From a reflection measurement in a rectangular microwave billiard with
randomly distributed scatterers the scattering and the ordinary fidelity was
studied. The position of one of the scatterers is the perturbation parameter.
Such perturbations can be considered as {\em local} since wave functions are
influenced only locally, in contrast to, e. g., the situation where the
fidelity decay is caused by the shift of one billiard wall. Using the
random-plane-wave conjecture, an analytic expression for the fidelity decay due
to the shift of one scatterer has been obtained, yielding an algebraic
decay for long times. A perfect agreement between experiment and theory has
been found, including a predicted scaling behavior concerning the dependence of
the fidelity decay on the shift distance. The only free parameter has been
determined independently from the variance of the level velocities.Comment: 4 pages, 5 figure
Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption
We quantify the presence of direct processes in the S-matrix of chaotic
microwave cavities with absorption in the one-channel case. To this end the
full distribution P_S(S) of the S-matrix, i.e. S=\sqrt{R}e^{i\theta}, is
studied in cavities with time-reversal symmetry for different antenna coupling
strengths T_a or direct processes. The experimental results are compared with
random-matrix calculations and with numerical simulations based on the
Heidelberg approach including absorption. The theoretical result is a
generalization of the Poisson kernel. The experimental and the numerical
distributions are in excellent agreement with random-matrix predictions for all
cases.Comment: 4 pages, 4 figure
Application of the Trace Formula in Pseudointegrable Systems
We apply periodic-orbit theory to calculate the integrated density of states
from the periodic orbits of pseudointegrable polygon and barrier
billiards. We show that the results agree so well with the results obtained
from direct diagonalization of the Schr\"odinger equation, that about the first
100 eigenvalues can be obtained directly from the periodic-orbit calculations
in good accuracy.Comment: 5 Pages, 4 Figures, submitted to Phys. Rev.
Quantum chaos and the double-slit experiment
We report on the numerical simulation of the double-slit experiment, where
the initial wave-packet is bounded inside a billiard domain with perfectly
reflecting walls. If the shape of the billiard is such that the classical ray
dynamics is regular, we obtain interference fringes whose visibility can be
controlled by changing the parameters of the initial state. However, if we
modify the shape of the billiard thus rendering classical (ray) dynamics fully
chaotic, the interference fringes disappear and the intensity on the screen
becomes the (classical) sum of intensities for the two corresponding one-slit
experiments. Thus we show a clear and fundamental example in which transition
to chaotic motion in a deterministic classical system, in absence of any
external noise, leads to a profound modification in the quantum behaviour.Comment: 5 pages, 4 figure
Weyl asymptotics: From closed to open systems
We present microwave experiments on the symmetry reduced 5-disk billiard
studying the transition from a closed to an open system. The measured microwave
reflection signal is analyzed by means of the harmonic inversion and the
counting function of the resulting resonances is studied. For the closed system
this counting function shows the Weyl asymptotic with a leading exponent equal
to 2. By opening the system successively this exponent decreases smoothly to an
non-integer value. For the open systems the extraction of resonances by the
harmonic inversion becomes more challenging and the arising difficulties are
discussed. The results can be interpreted as a first experimental indication
for the fractal Weyl conjecture for resonances.Comment: 9 pages, 7 figure
Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport
We investigate the transmission and reflection survival probabilities for the
chaotic stadium billiard with two holes placed asymmetrically. Classically,
these distributions are shown to have algebraic or exponential decays depending
on the choice of injecting hole and exact expressions are given for the first
time and confirmed numerically. As there is no reported quantum theoretical or
experimental analogue we propose a model for experimental observation of the
asymmetric transport using semiconductor nano-structures and comment on the
relevant quantum time-scales.Comment: 4 pages, 4 figure
Signatures of Dynamical Tunneling in the Wave function of a Soft-Walled Open Microwave Billiard
Evidence for dynamical tunneling is observed in studies of the transmission,
and wave functions, of a soft-walled microwave cavity resonator. In contrast to
previous work, we identify the conditions for dynamical tunneling by monitoring
the evolution of the wave function phase as a function of energy, which allows
us to detect the tunneling process even under conditions where its expected
level splitting remains irresolvable.Comment: 5 pages, 5 figure
Quasimodes of a chaotic elastic cavity with increasing local losses
We report non-invasive measurements of the complex field of elastic
quasimodes of a silicon wafer with chaotic shape. The amplitude and phase
spatial distribution of the flexural modes are directly obtained by Fourier
transform of time measurements. We investigate the crossover from real mode to
complex-valued quasimode, when absorption is progressively increased on one
edge of the wafer. The complexness parameter, which characterizes the degree to
which a resonance state is complex-valued, is measured for non-overlapping
resonances and is found to be proportional to the non-homogeneous contribution
to the line broadening of the resonance. A simple two-level model based on the
effective Hamiltonian formalism supports our experimental results
Energy localization in two chaotically coupled systems
We set up and analyze a random matrix model to study energy localization and
its time behavior in two chaotically coupled systems. This investigation is
prompted by a recent experimental and theoretical study of Weaver and Lobkis on
coupled elastomechanical systems. Our random matrix model properly describes
the main features of the findings by Weaver and Lobkis. Due to its general
character, our model is also applicable to similar systems in other areas of
physics -- for example, to chaotically coupled quantum dots.Comment: 20 pages, 15 figure
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