Critical exponents in metastable decay via quantum activation

TL;DR

This paper investigates how metastable states in a quantum oscillator decay near bifurcation points, revealing that decay occurs via quantum activation with a specific scaling law for decay probability.

Contribution

It introduces a new analysis of decay mechanisms near bifurcation points, identifying quantum activation as the dominant process and deriving the scaling exponent for decay probability.

Findings

Decay occurs via quantum activation over an effective barrier.

The decay probability scales as | ln W| extasciitilde eta^{\xi} near bifurcation points.

The scaling exponent  is derived for specific driven oscillators.

Abstract

We consider decay of metastable states of forced vibrations of a quantum oscillator close to bifurcation points, where dissipation becomes effectively strong. We show that decay occurs via quantum activation over an effective barrier. The decay probability $W$ scales with the distance $\eta$ to the bifurcation point as $|\ln W|\propto \eta^{\xi}$. The exponent $\xi$ is found for a resonantly driven oscillator and an oscillator modulated at nearly twice its eigenfrequency.