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

TL;DR

This paper investigates quantum wave packet dynamics in a nonstationary harmonic oscillator and demonstrates how periodic driving can significantly enhance escape rates from potential wells, with implications for reaction kinetics at low temperatures.

Contribution

It provides analytical solutions for wave packet energy increase under periodic modulation and links these to enhanced Kramers escape rates, especially near localized anharmonic vibrations.

Findings

Periodic driving can exponentially increase escape rates.

Resonance conditions amplify quantum escape phenomena.

Localized anharmonic vibrations facilitate catalytic effects.

Abstract

At sufficiently low temperatures, the reaction rates in solids are controlled by quantum rather than by thermal fluctuations. We solve the Schr\"odinger equation for a Gaussian wave packet in a nonstation-ary harmonic oscillator and derive simple analytical expressions for the increase of its mean energy with time induced by the time-periodic modulation. Applying these expressions to the modified Kra-mers theory, we demonstrate a strong increase of the rate of escape out of a potential well under the time-periodic driving, when the driving frequency of the well position equals its eigenfrequency, or when the driving 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 harmonic oscillations (phonons) that determine the system tem-perature. LAVs can be excited either thermally or by external triggering, which can result in strong catalytic effects due to amplification of the Kramers rate