# Quantum Markovian master equations: resonance theory shows validity for all time scales

## TL;DR

This paper proves that the quantum Markovian master equation remains valid for all time scales at small coupling strengths and introduces a new approximate dynamics that is asymptotically exact.

## Contribution

It demonstrates the universal validity of the Markov approximation for all times at small coupling and constructs a new semigroup dynamics that is asymptotically exact.

## Key findings

- Markov approximation valid for all times at small coupling
- Constructed a new asymptotically exact Markovian dynamics
- Established the validity of the master equation beyond previous time constraints

## Abstract

Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum sciences. The accuracy of the master equation approximation was so far proven for small values of the system-environment interaction coupling strength $\lambda$, under the additional constraint that time $t$ must not exceed an upper bound, $\lambda^2 t\le$ constant. Here, we show that the Markov approximation is valid for fixed small coupling strength and for all times. We also construct a new approximate Markovian dynamics -- a completely positive, trace preserving semigroup -- which is asymptotically in time exact, to all orders in the coupling.