  We present a new criterion, based on commutator methods, for the strong
mixing property of unitary representations of topological groups equipped with
a proper length function. Our result generalises and unifies recent results on
the strong mixing property of discrete flows $\{U^N\}_{N\in\mathbb Z}$ and
continuous flows $\{{\rm e}^{-itH}\}_{t\in\mathbb R}$ induced by unitary
operators $U$ and self-adjoint operators $H$ in a Hilbert space. As an
application, we present a short alternative proof (not using convolutions) of
the strong mixing property of the left regular representation of
$\sigma$-compact locally compact groups.
