The 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, and 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.

6 pages, 0 figures; v2 updated references; v3 updated references, extension to full-time and nonlocal regimes

References in corpus (3)

• Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
• The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
• Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation

Cited by in corpus (6)

• The equilibrium states of open quantum systems in the strong coupling regime
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit - divergences and resolution
• Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Effects of electron-phonon interaction on thermal and electrical transport through molecular nano-conductors
• Initial state preparation with dynamically generated system-environment correlations