  Quasicrystals (QCs) are a novel form of matter, which are neither crystalline
nor amorphous. Among many surprising properties of QCs is their high catalytic
activity. We propose a mechanism explaining this peculiarity based on unusual
dynamics of atoms at special sites in QCs, namely, localized anharmonic
vibrations (LAVs) and phasons. In the former case, one deals with a large
amplitude (~ fractions of an angstrom) time-periodic oscillations of a small
group of atoms around their stable positions in the lattice, known also as
discrete breathers, which can be excited in regular crystals as well as in QCs.
On the other hand, phasons are a specific property of QCs, which are
represented by very large amplitude (~angstrom) oscillations of atoms be-tween
two quasi-stable positions determined by the geometry of a QC. Large amplitude
atomic motion in LAVs and phasons results in time-periodic driving of adjacent
potential wells occupied by hydrogen ions (protons or deuterons) in case of
hydrogenated QCs. This driving may result in the increase of amplitude and
energy of zero-point vibrations (ZPV). Based on that, we demonstrate a drastic
increase of the D-D or D-H fusion rate with increasing number of modulation
periods evaluated in the framework of Schwinger model, which takes into account
suppression of the Coulomb barrier due to lattice vibrations. In this context,
we present numerical solution of Schrodinger equation for a particle in a
non-stationary double well potential, which is driven time-periodically
imitating the action of a LAV or phason. We show that the rate of tunneling of
the particle through the potential barrier separating the wells is enhanced
drastically by the driving, and it increases strongly with increasing amplitude
of the driving. These results support the concept of nuclear catalysis in QCs
that can take place at special sites provided by their inherent topology.
