Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model

Gonz�lez, J. Onam; Correa, Luis A.; Nocerino, Giorgio; Palao, Jos� P.; Alonso, Daniel; Adesso, Gerardo

Abstract

When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed locally on each component, i.e. ignoring the coherent couplings, which are later added ‘by hand’. Although simple, the resulting local master equation (LME) is known to be thermodynamically inconsistent. Otherwise, one may always obtain a consistent global master equation (GME) by working on the energy basis of the full interacting Hamiltonian. Here, we consider a two-node ‘quantum wire’connected to two heat baths. The stationary solution of the LME and GME are obtained and benchmarked against the exact result. Importantly, in our model, the validity of the GME is constrained by the underlying secular approximation. Whenever this breaks down (for resonant weakly-coupled nodes), we observe that the LME, in spite of being thermodynamically flawed: (a) predicts the correct steady state, (b) yields with the exact asymptotic heat currents, and (c) reliably reflects the correlations between the nodes. In contrast, the GME fails at all three tasks. Nonetheless, as the inter-node coupling grows, the LME breaks down whilst the GME becomes correct. Hence, the global and local approach may be viewed as complementary tools, best suited to different parameter regimes.

Citation

González, J. O., Correa, L. A., Nocerino, G., Palao, J. P., Alonso, D., & Adesso, G. (2017). Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model. Open Systems and Information Dynamics, 24(4), Article e1740010. https://doi.org/10.1142/S1230161217400108

• Journal Article Type: Article
• Acceptance Date: Aug 1, 2017
• Publication Date: Nov 30, 2017
• Deposit Date: Jan 25, 2018
• Publicly Available Date: Dec 1, 2018
• Journal: Open Systems & Information Dynamics
• Electronic ISSN: 1230-1612
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 4
• Article Number: e1740010
• DOI: https://doi.org/10.1142/S1230161217400108
• Public URL: https://nottingham-repository.worktribe.com/output/897312
• Publisher URL: http://www.worldscientific.com/doi/abs/10.1142/S1230161217400108
• Contract Date: Jan 25, 2018