Time local master equation connecting the Born and Markov approximations

Abstract

We present an exact expansion of the master equation for an open quantum system. The resulting equation is time local and enables us to calculate clearly defined higher order corrections to the Born-Markov approximation. In particular, we show that non-Markovian terms are of the same order of magnitude as higher order terms in the system-bath coupling. As a result we emphasize that analyzing non-Markovian behaviour of a system implies going beyond Born approximation. Additionally, we address with this approach the initial state problem occurring in non-Markovian master equations.

9 pages. 2 figure, published in Phys. Rev. B

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• Magnetic adatoms as memory bits: A quantum master equation analysis
• The connection between time-local and time-nonlocal perturbation expansions
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• Qubit quantum-dot sensors: noise cancellation by coherent backaction, initial slips, and elliptical precession
• Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime
• Non-Markovian correlation functions for open quantum systems
• Diagrammatic description of a system coupled strongly to a bosonic bath
• Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation
• Distortion of a reduced equilibrium density matrix: influence on quantum emulation
• Fermionic duality: General symmetry of open systems with strong dissipation and memory
• Reduced Dynamical Maps in Finite Temperature Vibronic Coupling Models via Choi Matrices: Numerical Methods and Applications