85 research outputs found
The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics
Considering a quantized chaotic system, we analyze the evolution of its
eigenstates as a result of varying a control parameter. As the induced
perturbation becomes larger, there is a crossover from a perturbative to a
non-perturbative regime, which is reflected in the structural changes of the
local density of states. For the first time the {\em full} scenario is explored
for a physical system: an Aharonov-Bohm cylindrical billiard. As we vary the
magnetic flux, we discover an intermediate twilight regime where perturbative
and semiclassical features co-exist. This is in contrast with the {\em simple}
crossover from a Lorentzian to a semicircle line-shape which is found in
random-matrix models.Comment: 4 pages, 4 figures, improved versio
Scaling properties of delay times in one-dimensional random media
The scaling properties of the inverse moments of Wigner delay times are
investigated in finite one-dimensional (1D) random media with one channel
attached to the boundary of the sample. We find that they follow a simple
scaling law which is independent of the microscopic details of the random
potential. Our theoretical considerations are confirmed numerically for systems
as diverse as 1D disordered wires and optical lattices to microwave waveguides
with correlated scatterers.Comment: 5 pages, 4 figures Submitted to Physical Review B Revision 2: 1)
Theoretical curve fits added to Figures 1-4. 2) Scaling parameter
added to inset of Figure 2. 3) Minor text changes to reflect
referee comments. 4) Some extra refereces were adde
Time delay in 1D disordered media with high transmission
We study the time delay of reflected and transmitted waves in 1D disordered media with high transmission. Highly transparent and translucent random media are found in nature or can be synthetically produced. We perform numerical simulations of microwaves propagating in disordered waveguides to show that reflection amplitudes are described by complex Gaussian random variables with the remarkable consequence that the time-delay statistics in reflection of 1D disordered media are described as in random media in the diffusive regime. For transmitted waves, we show numerically that the time delay is an additive quantity and its fluctuations thus follow a Gaussian distribution. Ultimately, the distributions of the time delay in reflection and transmission are physical illustrations of the central limit theorem at work
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