The ray picture
is not always adequate to describe resonances lifetimes in ARCs. Important
corrections may arise due to classically forbidden tunneling phenomena.
This can be studied in the
annular billiard, a circular resonator with a non-concentric inner
circle that cannot be penetrated. The outer circle could be a glass-air
interface, and the inner circle a metallic inclusion. In addition, we coated
the outer surface with a thin but penetrable metallic film to increase
all resonance lifetimes. The annular billiard with impenetrable outer
walls has been studied most recently by Doron and
Frischat,
as an example for the effects of chaos on tunneling processes. The work I
did with Gregor Hackenbroich shows that the leaky annular billiard
shows resonance lifetimes that fluctuate strongly with
deformation, due to
dynamical tunneling.
Shown below are the phase-space portraits of the annular billiard of the shape
indicated on the right. The false-color plot represents a metastable
wave function in the annular region between inner and outer circle,
projected onto the phase space. This representation is called a Husimi plot.
The highest weight in the first plot is concentrated on a region
where the classical dynamics is regular (not chaotic). For these
trajectories, it
is difficult to leak out of the resonator, so that the corresponding lifetime
is very long.
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