  For second countable discrete quantum groups, and more generally second
countable locally compact quantum groups with trivial scaling group, we show
that property (T) is equivalent to every weakly mixing unitary representation
not having almost invariant vectors. This is a generalization of a theorem of
Bekka and Valette from the group setting and was previously established in the
case of low dual by Daws, Skalsi, and Viselter. Our approach uses spectral
techniques and is completely different from those of Bekka--Valette and
Daws--Skalski--Viselter. By a separate argument we furthermore extend the
result to second countable nonunimodular locally compact quantum groups, which
are shown in particular not to have property (T), generalizing a theorem of
Fima from the discrete setting. We also obtain quantum group versions of
characterizations of property (T) of Kerr and Pichot in terms of the Baire
category theory of weak mixing representations and of Connes and Weiss in term
of the prevalence of strongly ergodic actions.
