Non-Markovianity over ensemble averages in quantum complex networks

TL;DR

This paper explores how the structure of bosonic quantum complex networks influences excitation transport and non-Markovianity, revealing that increasing interactions generally reduces non-Markovian effects, with tree networks being optimal.

Contribution

It provides a detailed analysis of the relationship between network structure, spectral density, and non-Markovianity in quantum harmonic oscillator networks, highlighting the impact of network topology.

Findings

Small structural changes significantly affect excitation transport.

Increasing network interactions suppresses average non-Markovianity.

Tree networks optimize non-Markovianity among random network types.

Abstract

We consider bosonic quantum complex networks as structured finite environments for a quantum harmonic oscillator and investigate the interplay between the network structure and its spectral density, excitation transport properties and non-Markovianity. After a review of the formalism used, we demonstrate how even small changes to the network structure can have a large impact on the transport of excitations. We then consider the non-Markovianity over ensemble averages of several different types of random networks of identical oscillators and uniform coupling strength. Our results show that increasing the number of interactions in the network tends to suppress the average non-Markovianity. This suggests that tree networks are the random networks optimizing this quantity.