  In many-body nonlinear systems with sufficient anharmonicity, a special kind
of lattice vibrations, namely, Localized Anharmonic Vibrations (LAV) can be
excited either thermally or by external triggering, in which the amplitude of
atomic oscillations greatly exceeds that of harmonic oscillations (phonons)
that determine the system temperature. Coherency and persistence of LAV may
have drastic effect on chemical and nuclear reaction rates due to time-periodic
modulation of reaction sites. One example is a strong acceleration of chemical
reaction rates driven by thermally-activated "jumps" over the reaction barrier
due to the time-periodic modulation of the barrier height in the LAV vicinity.
At sufficiently low temperatures, the reaction rate is controlled by quantum
tunneling through the barrier rather than by classical jumping over it. A giant
increase of sub-barrier transparency was demonstrated for a parabolic potential
well with the time-periodic eigenfrequency, when the modulation frequency
exceeds the eigenfrequency by a factor of ~2 (parametric regime). Such regime
can be realized for a hydrogen or deuterium atom in metal hydrides/deuterides,
such as NiH or PdD, in the vicinity of LAV. We present an analytical solution
of the Schrodinger equation for a nonstationary harmonic oscillator, analyze
the parametric regime in details and discuss its applications to the tunnel
effect and to D-D fusion in PdD lattice. We obtain simple analytical
expressions for the increase of amplitude and energy of zero-point oscillations
(ZPO) induced by the parametric modulation. Based on that, we demonstrate a
drastic increase of the D-D fusion rate with in-creasing number of modulation
periods evaluated in the framework of Schwinger model, which takes into account
suppression of the Coulomb barrier due to lattice vibrations.
