1Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom
2Institut für Physik und Astronomie, University of Potsdam, 14476 Potsdam, Germany.
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Abstract
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.
Featured image: Condition number of the matrices of the eigenvectors obtained by local and global master equations as a function of the inter-resonator coupling strength and the resonant frequency. A diverging condition number indicated by a brighter color demonstrates the presence of an exceptional point.
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Cited by
[1] Adam Hewgill, Gabriele De Chiara, and Alberto Imparato, “Quantum thermodynamically consistent local master equations”, Physical Review Research 3 1, 013165 (2021).
[2] Shishir Khandelwal, Nicolas Brunner, and Géraldine Haack, “Signatures of exceptional points in a quantum thermal machine”, arXiv:2101.11553.
[3] Roie Dann and Ronnie Kosloff, “Open system dynamics from thermodynamic compatibility”, Physical Review Research 3 2, 023006 (2021).
[4] Feng Tian, Jian Zou, Lei Li, Hai Li, and Bin Shao, “Effect of Inter-System Coupling on Heat Transport in a Microscopic Collision Model”, Entropy 23 4, 471 (2021).
[5] Gerard McCaul, Kurt Jacobs, and Denys I. Bondar, “Fast computation of dissipative quantum systems with ensemble rank truncation”, Physical Review Research 3 1, 013017 (2021).
[6] Anton Trushechkin, “Unified GKLS quantum master equation beyond the secular approximation”, arXiv:2103.12042.
The above citations are from SAO/NASA ADS (last updated successfully 2021-05-01 07:51:50). The list may be incomplete as not all publishers provide suitable and complete citation data.
Could not fetch Crossref cited-by data during last attempt 2021-05-01 07:51:48: Could not fetch cited-by data for 10.22331/q-2021-05-01-451 from Crossref. This is normal if the DOI was registered recently.
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