  The simplest models of inflation based on slow roll produce nearly scale
invariant primordial power spectra (PPS). But there are also numerous models
that predict radically broken scale invariant PPS. In particular, markedly
cuspy dips in the PPS correspond to nulls where the perturbation amplitude,
hence PPS, goes through a zero at a specific wavenumber. Near this wavenumber,
the true quantum nature of the generation mechanism of the primordial
fluctuations may be revealed. Naively these features may appear to arise from
fine tuned initial conditions. However, we show that this behavior arises under
fairly generic set of conditions involving super-Hubble scale evolution of
perturbation modes during inflation. We illustrate this with the well-studied
examples of punctuated inflation and the Starobinsky-break model.
