  It is widely accepted that structural glasses and disordered crystals exhibit
anomalies in the their thermal, mechanical and acoustic properties as
manifestations of the breakdown of the long-wavelength approximation in a
disordered dissipative environment. However, the same type of glassy-like
anomalies (i.e. boson peak in the vibrational density of states (VDOS) above
the Debye level, peak in the normalized specific heat at $T\simeq10 K$ etc)
have been recently observed also in perfectly ordered crystals, including
thermoelectric compounds. Here we present a theory that predicts these
surprising effects in perfectly ordered crystals as a result of low-lying
(soft) optical phonons. In particular, it is seen that a strong boson peak
anomaly (low-energy excess of modes) in the VDOS can be due almost entirely to
the presence of low-energy optical phonons, provided that their energy is
comparable to that of the acoustic modes at the Brillouin zone boundary. The
boson peak is predicted also to occur in the heat capacity at low $T$. In
presence of strong damping (which might be due to anharmonicities in the
ordered crystals), these optical phonons contribute to the low-$T$ deviation
from Debye's $T^{3}$ law, producing a linear-in-$T$ behavior which is typical
of glasses, even though no assumptions of disorder whatsoever are made in the
model. These findings are relevant for understanding and tuning thermal
transport properties of thermoelectric compounds, and possibly for the
enhancement of electron-phonon superconductivity.
