Quantum heat statistics with time-evolving matrix product operators

Maria Popovic, Mark Mitchison, Aidan Strathearn, Brendon W. Lovett, John Goold, Paul Eastham

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number020338
Number of pages18
JournalPRX Quantum
Issue number2
Publication statusPublished - 10 Jun 2021


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