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

González, J. Onam and Correa, Luis A. and Nocerino, Giorgio and Palao, José P. and Alonso, Daniel and Adesso, Gerardo (2017) Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model. Open Systems & Information Dynamics, 24 (04). e1740010. ISSN 1230-1612

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1142/S1230161217400108
Depositing User: Eprints, Support
Date Deposited: 25 Jan 2018 12:53
Last Modified: 22 Feb 2018 14:50
URI: http://eprints.nottingham.ac.uk/id/eprint/49330

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