Transition Path and Interface Sampling of Stochastic Schr\"odinger Dynamics

TL;DR

This paper applies transition path and interface sampling methods to stochastic Schr"odinger dynamics in open quantum systems, providing insights into rare transition mechanisms and quantifying rate constants, especially in quantum Brownian motion models.

Contribution

It extends transition path and interface sampling techniques to stochastic Schr"odinger equations, enabling analysis of rare events in open quantum systems.

Findings

Significant deviations from Arrhenius law at low temperatures.

Identification of anti-Zeno effect in quantum Brownian motion.

Quantitative measurement of transition rates in quantum systems.

Abstract

We study rare transitions in Markovian open quantum systems driven with Gaussian noise, applying transition path and interface sampling methods to trajectories generated by stochastic Schr\"odinger dynamics. Interface and path sampling offer insights into rare event transition mechanisms while simultaneously establishing a quantitative measure of the associated rate constant. Here, we extend their domain to systems described by stochastic Schr\"odinger equations. As a specific example, we explore a model of quantum Brownian motion in a quartic double well, consisting of a particle coupled to a Caldeira-Leggett oscillator bath, where we note significant departures from the Arrhenius law at low temperatures due to the presence of an anti-Zeno effect.