Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model
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 therm...
| Main Authors: | , , , , , |
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| Format: | Article |
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World Scientific Publishing
2017
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| Online Access: | https://eprints.nottingham.ac.uk/49330/ |
| _version_ | 1848797974625255424 |
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| author | González, J. Onam Correa, Luis A. Nocerino, Giorgio Palao, José P. Alonso, Daniel Adesso, Gerardo |
| author_facet | González, J. Onam Correa, Luis A. Nocerino, Giorgio Palao, José P. Alonso, Daniel Adesso, Gerardo |
| author_sort | González, J. Onam |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:12:24Z |
| format | Article |
| id | nottingham-49330 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:12:24Z |
| publishDate | 2017 |
| publisher | World Scientific Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-493302020-05-04T19:19:53Z https://eprints.nottingham.ac.uk/49330/ Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model González, J. Onam Correa, Luis A. Nocerino, Giorgio Palao, José P. Alonso, Daniel Adesso, Gerardo 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. World Scientific Publishing 2017-11-30 Article PeerReviewed González, J. Onam, Correa, Luis A., Nocerino, Giorgio, Palao, José P., 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 http://www.worldscientific.com/doi/abs/10.1142/S1230161217400108 doi:10.1142/S1230161217400108 doi:10.1142/S1230161217400108 |
| spellingShingle | González, J. Onam Correa, Luis A. Nocerino, Giorgio Palao, José P. Alonso, Daniel Adesso, Gerardo Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model |
| title | Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model |
| title_full | Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model |
| title_fullStr | Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model |
| title_full_unstemmed | Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model |
| title_short | Testing the validity of the ‘local’ and ‘global’ GKLS master equations on an exactly solvable model |
| title_sort | testing the validity of the ‘local’ and ‘global’ gkls master equations on an exactly solvable model |
| url | https://eprints.nottingham.ac.uk/49330/ https://eprints.nottingham.ac.uk/49330/ https://eprints.nottingham.ac.uk/49330/ |