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Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green’s function approach

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Abstract

This paper presents a Green’s function-based root locus method to investigate the boundary between Markovian and non-Markovian open quantum systems in the frequency domain. A Langevin equation for the boson-boson coupling system is derived, where we show that the structure of the Green’s function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, the system dynamics are driven from Markovian to non-Markovian dynamics, which results from the redistribution in the modes of the Green’s function in the frequency domain. Both a critical transition and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.

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Acknowledgments

This research was supported by the Australian Research Council under grant FL110100020. Re-Bing Wu acknowledges support from TNlist and Natural Science Foundation of China (Grant Nos. 61374091 and 61134008).

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Authors and Affiliations

  1. School of Engineering and Information Technology, UNSW Canberra at the Australian Defence Force Academy, Northcott Drive, Campbell ACT, 2600, Australia

    Shibei Xue & Ian R. Petersen

  2. Department of Automation, Tsinghua University, Beijing, 100084, People’s Republic of China

    Rebing Wu

  3. Department of Electrical and Systems Engineering, Washington University St. Louis, St. Louis, MO, 63130, USA

    Tzyh-Jong Tarn

Authors
  1. Shibei Xue
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  2. Rebing Wu
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  3. Tzyh-Jong Tarn
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  4. Ian R. Petersen
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Correspondence to Shibei Xue.

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Xue, S., Wu, R., Tarn, TJ. et al. Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green’s function approach. Quantum Inf Process 14, 2657–2672 (2015). https://doi.org/10.1007/s11128-015-1000-6

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  • DOI: https://doi.org/10.1007/s11128-015-1000-6

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