  We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg
exciton systems. Using analytical and numerical arguments we demonstrate that
this coupling considerably modifies the wave functions and leads to a level
repulsion that results in a deviation from the Poissonian statistics of the
adjacent level distance distribution. This signifies the crossover to
non-integrability of the system and hints on the possibility of quantum chaos
emerging. Such a behavior strongly differs from the classical realization,
where spin-orbit coupling produces highly entangled, chaotic electron
trajectories in an exciton. We also calculate the oscillator strengths and show
that randomization appears in the transitions between states with different
total momenta.
