Qubit-mediated energy transfer between thermal reservoirs: beyond Markovian Master equation

TL;DR

This paper investigates energy transfer between two electron reservoirs mediated by a qubit using a numerically-exact method, revealing limitations of traditional Markovian approaches at intermediate coupling strengths.

Contribution

It introduces a non-perturbative, numerically-exact influence functional path-integral method to study qubit-mediated energy transfer beyond weak coupling regimes.

Findings

Markovian Master equation predictions deviate significantly at intermediate coupling.

Exact simulations show the breakdown of weak-coupling assumptions.

Caution is advised when applying Markovian models beyond weak coupling.

Abstract

We study qubit-mediated energy transfer between two electron reservoirs by adopting a numerically-exact influence functional path-integral method. This non-perturbative technique allows us to study the system's dynamics beyond the weak coupling limit. Our simulations for the energy current indicate that perturbative-Markovian Master equation predictions significantly deviate from exact numerical results already at intermediate coupling, $\pi \rho \alpha_{j,j'}\gtrsim 0.4$, where $\rho$ is the metal (Fermi sea) density of states, taken as a constant, and $\alpha_{j,j'}$ is the scattering potential energy of electrons, between the $j$ and $j'$ states. Markovian Master equation techniques should be therefore used with caution beyond the strictly weak subsystem-bath coupling limit, especially when a quantitative knowledge of transport characteristics is desired.