# Quantum resonant activation

## TL;DR

This paper investigates quantum resonant activation in a driven two-state system with strong dissipation, revealing a minimum in mean first passage time at a specific modulation frequency through analytical and numerical methods.

## Contribution

It provides a detailed analysis of quantum resonant activation phenomena, including the behavior of first passage times under both random and periodic driving, and identifies a critical frequency for resonance.

## Key findings

- Minimum mean first passage time at a specific modulation frequency
- Complex multi-peaked first passage time distribution under periodic driving
- Critical frequency for resonance weakly dependent on driving strength

## Abstract

Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probability density function (pdf) displays a complex, multi-peaked behavior, which depends crucially on the details of initial phase, frequency, and strength of the driving. As an interesting feature we find that the mean first passage time enters the resonant activation regime at a critical frequency $\nu^*$ which depends very weakly on the strength of the driving. Moreover, we provide the relation between the first passage time pdf and the statistics of residence times.