Quantum-classical crossover of the transition rate in the damped double well

Abstract

The author studies the barrier-crossing rate Gamma for a particle in a symmetric double well coupled to a sluggish bath; the aim is to justify the quantum simulation procedure used in related work on the diffusion of hydrogen in metals. He uses path-integral methods to discuss the transition between the low-temperature tunnelling and the high-temperature barrier-jumping regimes, and suggests a unifying formula valid for both, which relates Gamma to the probability of finding the centroid of the quantum path at the barrier top. Numerical results for Gamma are presented for the case of the quartic double well.