R. de la Llave, N. Petrov
Theory of Circle Maps and the Problem of One-Dimensional Optical
Resonator with a Periodically Moving Wall
(279K, LaTeX (RevTeX) with 6 EPS figures)
ABSTRACT. We consider the electromagnetic field in a cavity
with a periodically oscillating
perfectly reflecting boundary
and show that the mathematical
theory of circle maps leads
to several physical predictions.
Notably, well-known results
in the theory of circle maps
(which we review briefly)
imply that there are intervals
of parameters where the waves in the
cavity get concentrated in wave packets
whose energy grows exponentially.
Even if these intervals are dense
for typical motions of the reflecting boundary,
in the complement there is a
positive measure set of parameters
where the energy remains bounded.