Heat flux dynamics in dissipative cascaded systems

TL;DR

This paper investigates the non-Markovian heat flux dynamics in dissipative cascaded quantum systems, revealing how initial correlations and system type influence thermalization behavior.

Contribution

It introduces a detailed analysis of heat flux in cascaded quantum systems, highlighting the impact of initial correlations and contrasting harmonic oscillators with qubits.

Findings

Heat flux exhibits non-exponential behavior due to non-Markovian dynamics.

Initial correlations significantly affect heat flux rates.

Trace distance discord relates to correlated heat flux contributions in qubits.

Abstract

We study the dynamics of heat flux in the thermalization process of a pair of identical quantum system that interact dissipatively with a reservoir in a {\it cascaded} fashion. Despite the open dynamics of the bipartite system S is globally Lindbladian, one of the subsystems "sees" the reservoir in a state modified by the interaction with the other subsystem and hence it undergoes a non-Markovian dynamics. As a consequence, the heat flow exhibits a non-exponential time behaviour which can greatly deviate from the case where each party is independently coupled to the reservoir. We investigate both thermal and correlated initial states of $S$ and show that the presence of correlations at the beginning can considerably affect the heat flux rate. We carry out our study in two paradigmatic cases -- a pair of harmonic oscillators with a reservoir of bosonic modes and two qubits with a reservoir of fermionic modes -- and compare the corresponding behaviours. In the case of qubits and for initial thermal states, we find that the trace distance discord is at any time interpretable as the correlated contribution to the total heat flux.