  Using an analogy between the conductivity tensor of electronic systems and
the spin stiffness tensor of spin systems, we introduce the concept of the
Thouless number $g_0$ and the dimensionless frequency dependent conductance $g(
\omega )$ for quantum spin models. It is shown that spin diffusion implies the
vanishing of the Drude peak of $g ( \omega )$, and that the spin diffusion
coefficient $D_s$ is proportional to $g_0$. We develop a new method based on
the Thouless number to calculate $D_s$, and present results for $D_s$ in the
nearest-neighbor quantum Heisenberg ferromagnet at infinite temperatures for
arbitrary dimension $d$ and spin $S$.
