title: Accuracy of perturbative master equations.
abstract: We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
authors.affiliation: Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: C H
authors.initials: CH
authors.lastname: Fleming
authors.forename: N I
authors.initials: NI
authors.lastname: Cummings
mesh_terms: D008390:Markov Chains; D008433:Mathematics; D015233:Models, Statistical; D008962:Models, Theoretical; D011789:Quantum Theory; D015203:Reproducibility of Results; D013598:Systems Theory; D013696:Temperature