  Using molecular dynamics simulations we analyze the dynamics of two atomic
liquids that display a liquid-liquid phase transition (LLPT): Si described by
the Stillinger-Weber potential and Ga as modeled by the modified embedded-atom
model (MEAM). In particular, our objective is to investigate the extent to
which the presence of a dip in the self-intermediate scattering function is a
manifestation of an excess of vibrational states at low frequencies and may be
associated with a fragile-to-strong transition (FTST) across the LLPT, as
suggested recently. Our results do not lend support to these suggestions.
Specifically, in the case of Ga we observe the appearance of an excess of
vibrational states at low frequencies, even in the absence of the appearance of
a dip in the self-intermediate scattering function across the LLPT.
Furthermore, studying the behavior of the shear viscosities traversing the
LLPTs we find that, despite the development of a dip in the self-intermediate
scattering function for the case of Si and its absence in Ga, both substances
are fragile in character above and below their respective LLPT temperatures.
