# Non-monotonic population and coherence evolution in Markovian open-system dynamics

## TL;DR

This paper investigates a Markovian qubit model where non-monotonic population and coherence dynamics emerge due to non-secular effects, challenging typical associations between Markovianity and monotonic behavior.

## Contribution

It demonstrates how non-monotonic evolution can occur in Markovian systems through non-secular contributions and shows how similar effects can be mimicked with memory effects in phase covariant models.

## Key findings

- Non-monotonic population dynamics observed in Markovian qubit model.
- Non-secular effects cause coherence revival despite Markovianity.
- Memory effects can replicate non-monotonic behavior in phase covariant evolutions.

## Abstract

We consider a simple microscopic model where the open-system dynamics of a qubit, despite being Markovian, shows features which are typically associated to the presence of memory effects. Namely, a non monotonic behavior both in the population and in the coherence evolution arises due to the presence of non-secular contributions, which break the phase covariance of the Lindbladian (semigroup) dynamics. We also show by an explicit construction how such a non-monotonic behaviour can be reproduced by a phase covariant evolution, but only at the price of inserting some state-dependent memory effects.