Like the amplitudes, the (discrete)
nonnegative measures (probabilities to be
located at a site)
$$
p_{u,v}(\bk, T)=u^\dagger a(\bk,T) v^2
$$
oscillate wildly.
When rescaled, the sqared absolute values of the
amplitudes weakly converge to certain probability measure
as $T\to\infty$,
$$
p_{u,v}(\lfloor T\bp\rfloor, T)\to
\limmes_{u,v}.
$$

