We will show that some classical zero entropy sequences are not only
orthogonal to all multiplicative (arithmetic) functions but the
orthogonality takes also place on "typical" short intervals. For example
$$
\frac1M\sum_{M\leq m<2M}\left| \frac1H\sum_{m\leq h<m+H}
e^{2\pi i P(n)}u(n)\right|\to 0
$$
when $H\to\infty$, $H/M\to 0$. Here $P\in\mathbb R[x]$ is a non-constant
polynomial
with irrational leading coefficient and $u:\mathbb N\to\mathbb C$ is an arbitrary
multiplicative function, $|u|\leq1$.
To prove the above result we use a new joining property of automorphisms
in ergodic theory,
called Asymptotically Orthogonal Powers (AOP). It holds for example for
quasi-discrete (Abramov) automorphisms
and in general allows one to study certain asyptotic properties of
observables in uniquely ergodic models of zero entropy systems.