How general are time-local master equations?

Abstract

Time-local master equations are more generally applicable than is often recognised, but at first sight it would seem that they can only safely be used in time intervals where the time evolution is invertible. Using the Jaynes-Cummings model, we here construct an explicit example where two different Hamiltonians, corresponding to two different non-invertible and non-Markovian time evolutions, will lead to arbitrarily similar time-local master equations. This illustrates how the time-local master equation on its own in this case does not uniquely determine the time evolution. The example is nevertheless artificial in the sense that a rapid change in (at least) one of the Hamiltonians is needed. The change must also occur at a very specific instance in time. If a Hamiltonian is known not to have such very specific behaviour, but is "physically well-behaved", then one may conjecture that a time-local master equation also determines the time evolution when it is not invertible.

7 pages, 6 figures

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• Non-Markovian dynamics under time-translation symmetry
• Invertibility as a witness of Markovianity of the quantum dynamical maps
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• Revisiting the Jaynes-Cummings model with time-dependent coupling
• Non-Markovian Light-Matter Dynamics in the Time Fractional Jaynes-Cummings Model with Modulated Coupling
• Reproducing the effects of quantum deformation in the undeformed Jaynes-Cummings model
• Open quantum dynamics with singularities: Master equations and degree of non-Markovianity
• On the modeling of irreversibility by relaxator Liouville dynamics