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Modelling Non-Markovian Quantum Systems Using Tensor Networks

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Abstract

In this chapter, the methods described in the previous chapter for numerically evaluating time ordered expressions are applied to study three simple models of open quantum systems that exhibit non-Markovian phenomena. First, the localisation phase transition in the Spin-Boson model is studied in Sect. 4.1, where it is shown that the location of the transition can be identified numerically to produce results consistent with existing literature. Localisation is non-Markovian by nature since it involves infinite ranged memory effects. In Sect. 4.2 the phenomenon of environment mediated interactions is investigated in a model of two spins interacting with a common environment. In this model the propagation of environmental excitations between the spins is nontrivial non-Markovian behaviour that is not possible to capture using existing methods, and the results presented in Sect. 4.2 are the first to confirm that the system behaves in an intuitive manner

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Queensland, Brisbane, QLD, Australia

    Dr. Aidan Strathearn

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  1. Dr. Aidan Strathearn
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Correspondence to Aidan Strathearn .

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Strathearn, A. (2020). Results. In: Modelling Non-Markovian Quantum Systems Using Tensor Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-54975-6_4

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