  We have studied the static and dynamic properties of quasi-two-dimensional
quantum antiferromagnets (AF) diluted with spinless impurities using spin-wave
theory and $T$-matrix approximation. We show that the spectrum of a 2D AF at
long wavelengths is overdamped at arbitrary concentration of spinless
impurities. The scattering leads to a new length scale $\ell/a \sim
e^{\pi/4x}$, $x$ being impurity concentration and $a$ the lattice spacing,
beyond which the influence of impurities on the spectrum is dominant. Although
the dynamical properties are significantly modified we show that 2D is not the
lower critical dimension for this problem. Thus, in low-dimensional systems
with disorder the connection between static and dynamic quantities is not
straightforward. Our results are in quantitative agreement with the recent
Monte Carlo simulations and experimental data for $S=1/2$, S=1, and $S=5/2$. We
have also proposed experiments which can further test the results of our
theory.
