Long-time memory in non-Markovian evolutions

TL;DR

This paper explores how non-Markovian quantum dynamics retain memory of initial states and entanglement, affecting the asymptotic behavior and invariance of equilibrium states, revealing key signatures of non-Markovianity.

Contribution

It clarifies the relationship between non-Markovianity, memory effects, and the invariance of equilibrium states in open quantum systems.

Findings

Asymptotic states depend on initial conditions in non-Markovian dynamics.

Equilibrium states in non-Markovian systems may not be invariant.

Memory effects can preserve initial entanglement in the long-term.

Abstract

If the dynamics of an open quantum systems is non-Markovian, its {asymptotic} state strongly depends on the initial conditions, even if the dynamics possesses an {invariant} state. This is the very essence of memory effects. In particular, the {asymptotic} state can remember and partially preserve its initial entanglement. Interestingly, even if the non-Markovian evolution relaxes to an equilibrium state, this state needs not be invariant. Therefore, the non-invariance of equilibrium becomes a clear sign of non-Markovianity.