Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation

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Research units

  • CSIC UIB, Consejo Superior de Investigaciones Cientificas (CSIC), Universitat de les Illes Balears, CSIC-UIB - Instituto de Fisica Interdisciplinar y Sistemas Complejos (IFISC), University of Barcelona, IFISC
  • Univ Turku, University of Turku, Dept Phys & Astron, Turku Ctr Quantum Phys, QTF Ctr Excellence


Open systems of coupled qubits are ubiquitous in quantum physics. Finding a suitable master equation to describe their dynamics is therefore a crucial task that must be addressed with utmost attention. In the recent past, many efforts have been made toward the possibility of employing local master equations, which compute the interaction with the environment neglecting the direct coupling between the qubits, and for this reason may be easier to solve. Here, we provide a detailed derivation of the Markovian master equation for two coupled qubits interacting with common and separate baths, considering pure dephasing as well as dissipation. Then, we explore the differences between the local and global master equation, showing that they intrinsically depend on the way we apply the secular approximation. Our results prove that the global approach with partial secular approximation always provides the most accurate choice for the master equation when Born?Markov approximations hold, even for small inter-system coupling constants. Using different master equations we compute the stationary heat current between two separate baths, the entanglement dynamics generated by a common bath, and the emergence of spontaneous synchronization, showing the importance of the accurate choice of approach.


Original languageEnglish
Article number113045
Number of pages23
JournalNew Journal of Physics
Issue number11
Publication statusPublished - Nov 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • Markovian master equation, secular approximation, coupled qubits, common and separate baths, OPEN-SYSTEM, QUANTUM, QUBITS, TRANSPORT, DYNAMICS, MEMORY

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