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arXiv:1802.03678 · Physics Letters A

Boson–boson pure-dephasing model with non-Markovian properties

Fei-Lei Xiong, Li Li, Zeng-Bing Chen

Published Oct 23, 2018• 4 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2018.10.022

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We evaluate the non-Markovian finite-temperature two-time correlation functions (CF's) of system operators of a pure-dephasing spin-boson model in two different ways, one by the direct exact operator technique and the other by the recently derived evolution equations, valid to second order in the system-environment interaction Hamiltonian. This pure-dephasing spin-boson model that is exactly solvable has been extensively studied as a simple decoherence model. However, its exact non-Markovian finite-temperature two-time system operator CF's, to our knowledge, have not been presented in the literature. This may be mainly due to the fact, illustrated in this article, that in contrast to the Markovian case, the time evolution of the reduced density matrix of the system (or the reduced quantum master equation) alone is not sufficient to calculate the two-time system operator CF's of non-Markovian open systems. The two-time CF's obtained using the recently derived evolution equations in the weak system-environment coupling case for this non-Markovian pure-dephasing model happen to be the same as those obtained from the exact evaluation. However, these results significantly differ from the non-Markovian two-time CF's obtained by wrongly directly applying the quantum regression theorem (QRT), a useful procedure to calculate the two-time CF's for weak-coupling Markovian open systems. This demonstrates clearly that the recently derived evolution equations generalize correctly the QRT to non-Markovian finite-temperature cases. It is believed that these evolution equations will have applications in many different branches of physics.
We study quantum dissipative dynamics of entanglement in the spin-boson model, described by the generalized master equation. We consider the two opposite limits of pure-dephasing and relaxation models, measuring the degree of entanglement with the concurrence. When the Markovian approximation is employed, entanglement is shown to decay exponentially in both cases. On the other hand, non-Markovian contributions alter the analytic structure of the master equation, resulting in logarithmic decay in the pure dephasing model.
ABSTRACT The spin‐boson model's dynamical and thermodynamic features in the weak coupling regime are investigated using the weak coupling spin‐boson (WCSB) and phase covariant (PC) master equations. Both unital (pure dephasing) and non‐unital (dissipative) quantum channels are considered. On the dynamical side, key quantum features including non‐Markovianity, quantum speed limit, quantum coherence, and the system's steady‐state behavior, are explored. Notably, the measures of non‐Markovianity exhibit different behavior under WCSB and PC dynamics. From the quantum thermodynamic perspective, the spin‐boson system is conceptualized as a quantum battery and analyze its performance through metrics such as energy, ergotropy, anti‐ergotropy, and battery capacity. The roles of pure dephasing and dissipative processes in shaping the battery's performance are further examined. The findings demonstrate the spin‐boson model's versatility as a platform for efficient energy storage and transfer in quantum thermodynamic devices.