Local master equations bypass the secular approximation

Quantum 5, 451 (2021).

https://doi.org/10.22331/q-2021-05-01-451

Master equations are a vital tool to model heat flow through nanoscale thermodynamic systems. Most practical devices are made up of interacting sub-system, and are often modelled using either $textit{local}$ master equations (LMEs) or $textit{global}$ master equations (GMEs). While the limiting cases in which either the LME or the GME breaks down are well understood, there exists a ‘grey area’ in which both equations capture steady-state heat currents reliably, but predict very different $textit{transient}$ heat flows. In such cases, which one should we trust? Here, we show that, when it comes to dynamics, the local approach can be more reliable than the global one for weakly interacting open quantum systems. This is due to the fact that the $textit{secular approximation}$, which underpins the GME, can destroy key dynamical features. To illustrate this, we consider a minimal transport setup and show that its LME displays $textit{exceptional points}$ (EPs). These singularities have been observed in a superconducting-circuit realisation of the model [1]. However, in stark contrast to experimental evidence, no EPs appear within the global approach. We then show that the EPs are a feature built into the Redfield equation, which is more accurate than the LME and the GME. Finally, we show that the local approach emerges as the weak-interaction limit of the Redfield equation, and that it entirely avoids the secular approximation.