Quantum heat statistics with time-evolving matrix product operators
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We present a numerically exact method to compute the full counting statistics of heat transfer in non-Markovian open quantum systems, which is based on the time-evolving matrix product operator (TEMPO) algorithm. This approach is applied to the paradigmatic spin-boson model in order to calculate the mean and fluctuations of the heat transferred to the environment during thermal equilibration. We show that system-reservoir correlations make a significant contribution to the heat statistics at low temperature and present a variational theory that quantitatively explains our numerical results. We also demonstrate a fluctuation-dissipation relation connecting the mean and variance of the heat distribution at high temperature. Our results reveal that system-bath interactions make a significant contribution to heat transfer even when the dynamics of the open system is effectively Markovian. The method presented here provides a flexible and general tool to predict the fluctuations of heat transfer in open quantum systems in non-perturbative regimes.
Popovic , M , Mitchison , M , Strathearn , A , Lovett , B W , Goold , J & Eastham , P 2021 , ' Quantum heat statistics with time-evolving matrix product operators ' , PRX Quantum , vol. 2 , no. 2 , 020338 . https://doi.org/10.1103/PRXQuantum.2.020338
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DescriptionFunding: We acknowledge funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program (ODYSSEY Grant Agreement No. 758403). J.G.is grateful for support from a SFI-Royal Society University Research Program. We also acknowledge support from the EPSRC, under Grant No. EP/T014032/1. A.S. acknowledges support the Australian Research Council Centres of Excellence for Engineered Quantum Systems (EQUS, CE170100009).
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