Markovian master equations for quantum thermal machines: local versus global approach

By P. Hofer, M. Perarnau-Llobet, L David M Miranda, G. Haack, Ralph Silva, Jonatan Bohr Brask, Nicolas Brunner. 2017

282 citations recorded by the source corpus.

The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0ed3d4abdd81b77e7873e95081dde2094a2201d1

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Jukka P. Pekola

In Statistical and Nonlinear Physics

Citations in the corpus

Introduction to Quantum Thermodynamics: History and Prospects (2018, background): “ the links are identical the secular approximation may fail for vanishing small links. In these cases local GKLS equations give the correct heat current with respect to numerical converged approaches [60, 61, 62]. General conditions of adding up consistently GKLS generators have been suggested [63].”
Colloquium : Quantum heat transport in condensed matter systems (2021, background): “…measurement of heat transport in such a circuit addresses some fundamental questions of open quantum systems (Aurell and Montana, 2019; Chiara et al., 2018; Donvil et al., 2020, 2018; Hewgill et al., 2020; Hofer et al., 2017; Levy and Kosloff, 2014; Magazzù and Grifoni, 2019; Rivas et al., 2010).”