37 research outputs found
Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents
We study fidelity decay in classically chaotic microwave billiards for a local, piston-like boundary perturbation. We experimentally verify a predicted non-monotonic cross-over from the Fermi Golden Rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations
Probing Localization in Absorbing Systems via Loschmidt Echos
We measure Anderson localization in quasi-one-dimensional waveguides in the
presence of absorption by analyzing the echo dynamics due to small
perturbations. We specifically show that the inverse participation number of
localized modes dictates the decay of the Loschmidt echo, differing from the
Gaussian decay expected for diffusive or chaotic systems. Our theory, based on
a random matrix modeling, agrees perfectly with scattering echo measurements on
a quasi one-dimensional microwave cavity filled with randomly distributed
scatterers.Comment: cross-reference with nonlin.CD-Chaotic Dynamic
Experimental Observation of Resonance-Assisted Tunneling
We present the first experimental observation of resonance-assisted
tunneling, a wave phenomenon, where regular-to-chaotic tunneling is strongly
enhanced by the presence of a classical nonlinear resonance chain. For this we
use a microwave cavity made of oxygen free copper with the shape of a
desymmetrized cosine billiard designed with a large nonlinear resonance chain
in the regular region. It is opened in a region, where only chaotic dynamics
takes place, such that the tunneling rate of a regular mode to the chaotic
region increases the line width of the mode. Resonance-assisted tunneling is
demonstrated by (i) a parametric variation and (ii) the characteristic plateau
and peak structure towards the semiclassical limit.Comment: 5 pages, 2 figure
Generalized Berry Conjecture and mode correlations in chaotic plates
We consider a modification of the Berry Conjecture for eigenmode statistics
in wave-bearing systems. The eigenmode correlator is conjectured to be
proportional to the imaginary part of the Green's function. The generalization
is applicable not only to scalar waves in the interior of homogeneous isotropic
systems where the correlator is a Bessel function, but to arbitrary points of
heterogeneous systems as well. In view of recent experimental measurements,
expressions for the intensity correlator in chaotic plates are derived.Comment: 5 pages, 1 figur
Bose-Einstein condensates on tilted lattices: coherent, chaotic and subdiffusive dynamics
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein
condensate in a tilted optical lattice is studied in a discrete mean-field
approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation.
If the static field is varied the system shows a plethora of dynamical
phenomena. In the strong field limit we demonstrate the existence of (almost)
non-spreading states which remain localized on the lattice region populated
initially and show coherent Bloch oscillations with fractional revivals in the
momentum space (so called quantum carpets). With decreasing field, the dynamics
becomes irregular, however, still confined in configuration space. For even
weaker fields we find sub-diffusive dynamics with a wave-packet width spreading
as .Comment: 4 pages, 5 figure
Fano resonances and decoherence in transport through quantum dots
A tunable microwave scattering device is presented which allows the
controlled variation of Fano line shape parameters in transmission through
quantum billiards. We observe a non-monotonic evolution of resonance parameters
that is explained in terms of interacting resonances. The dissipation of
radiation in the cavity walls leads to decoherence and thus to a modification
of the Fano profile. We show that the imaginary part of the complex Fano
q-parameter allows to determine the absorption constant of the cavity. Our
theoretical results demonstrate further that the two decohering mechanisms,
dephasing and dissipation, are equivalent in terms of their effect on the
evolution of Fano resonance lineshapes.Comment: 9 pages, 7 figures, submitted to Physica E (conference proceedings
Microwave experiments simulating quantum search and directed transport in artificial graphene
A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to \sqrt{N}, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover’s original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density—namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains
Survival Probability of a Doorway State in regular and chaotic environments
We calculate survival probability of a special state which couples randomly
to a regular or chaotic environment. The environment is modelled by a suitably
chosen random matrix ensemble. The exact results exhibit non--perturbative
features as revival of probability and non--ergodicity. The role of background
complexity and of coupling complexity is discussed as well.Comment: 19 pages 5 Figure
Energy Spectrum Evolution of a Diffuse Field in Elastic Body Caused by Weak Nonlinearity
We study the evolution of diffuse elastodynamic spectral energy density under
the influence of weak nonlinearity. It is shown that the rate of change of this
quantity is given by a convolution of the linear energy at two frequencies.
Quantitative estimates are given for sample aluminum and fused silica blocks of
experimental interest.Comment: 9 pages, 3 figures; revised for better presentatio