  We perform time-dependent analysis of quantum dynamics of dark matter
particles in the Solar System. It is shown that this problem has similarities
with a microwave ionization of Rydberg atoms studied previously experimentally
and analytically. On this basis it is shown that the quantum effects for
chaotic dark matter dynamics become significant for dark matter mass ratio to
electron mass being smaller than $2 \times 10^{-15}$. Below this border
multiphoton diffusion over Rydberg states of dark matter atom becomes
exponentially localized in analogy with the Anderson localization in disordered
solids. The life time of dark matter in the Solar System is determined in
dependence on mass ratio in the localized phase and a few photon ionization
regime. The quantum effects for dark matter captured by other binary systems
are also discussed.
