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International Journal of Theoretical Physics

Nakajima-Zwanzig and Time-Convolutionless Master Equations for a One-Qubit System in a Non-Markovian Layered Environment

M. Mahdian, Hadi Mehrabpour

Published Apr 2, 2014• 1 citation
Publisher
DOI
10.1007/s10773-014-2075-z

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The driven two-level system is a useful model to describe many quantum objects, particularly in quantum information processing. However, the exact master equation for such a system has barely been explored. Making use of the Feynman-Vernon influence functional theory, we derive an exact non-Markovian master equation for the driven two-level system and show the lost feature in the perturbative treatment for this system. The perturbative treatment leads to the time-convolutionless (TCL) and Nakajima-Zwanzig (NZ) master equations. So to this end we derive the TCL and NZ master equations for the system and compare the dynamics given by the three master equations. We find the validity condition for the TCL and NZ master equations. Based on the exact non-Markovian master equation, we analyze the regime of validity for the secular approximation in the time-convolutionless master equation and discuss the leading corrections of the nonsecular terms to the quantum dynamics. Significant effects are found in the dynamics of the driven system.
In the framework of the dissipative dynamics of coupled qubits interacting with independent reservoirs, a comparison between non-Markovian master equation techniques and an exact solution is presented here. We study various regimes in order to find the limits of validity of the Nakajima–Zwanzig and the time-convolutionless master equations in the description of the entanglement dynamics. A comparison between the performances of the concurrence and the negativity as entanglement measures for the system under study is also presented.