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At sufficiently low temperatures, the reaction rates in solids are controlledby quantum rather than by thermal fluctuations. We solve the Schr\"odingerequation for a Gaussian wave packet in a nonstation-ary harmonic oscillator andderive simple analytical expressions for the increase of its mean energy withtime induced by the time-periodic modulation. Applying these expressions to themodified Kra-mers theory, we demonstrate a strong increase of the rate ofescape out of a potential well under the time-periodic driving, when thedriving frequency of the well position equals its eigenfrequency, or when thedriving frequency of the well width exceeds its eigenfrequency by a factor of~2. Such re-gimes can be realized near localized anharmonic vibrations (LAVs),in which the amplitude of atomic oscillations greatly exceeds that of harmonicoscillations (phonons) that determine the system tem-perature. LAVs can beexcited either thermally or by external triggering, which can result in strongcatalytic effects due to amplification of the Kramers rate

Quantum dynamics of wave packets in a nonstationary parabolic potential and the Kramers escape rate theory