  In recent years fractal Weyl laws and related quantum eigenfunction
hypothesis have been studied in a plethora of numerical model systems, called
quantum maps. In some models studied there one can easily prove uniform
hyperbolicity. Yet, a numerically sound method for computing quantum resonance
states, did not exist. To address this challenge, we recently introduced a new
class of quantum maps. For these quantum maps, we showed that, quantum
resonance states can numerically be computed using theoretically grounded
methods such as complex scaling or weak absorbing potentials. However, proving
uniform hyperbolicty for this class of quantum maps was not straight forward.
Going beyond that work this article generalizes the class of scattering maps
and provides mathematical proofs for their uniform hyperbolicity. In
particular, we show that the suggested class of two-dimensional symplectic
scattering maps satisfies the topological horseshoe condition and uniform
hyperbolicity. In order to prove these properties, we follow the procedure
developed in the paper by Devaney and Nitecki. Specifically, uniform
hyperbolicity is shown by identifying a proper region in which the
non-wandering set satisfies a sufficient condition to have the so-called sector
bundle or cone field. Since no quantum map is known where both a proof of
uniform hyperbolicity and a methodologically sound method for numerically
computing quantum resonance states exist simultaneously, the present result
should be valuable to further test fractal Weyl laws and related topics such as
chaotic eigenfunction hypothesis.
