Abstract
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.
Highlights
The importance of heat management at the nanoscale has grown in tandem with advances in the fabrication and control of small devices, motivating increasing interest in the nonequilibrium thermodynamics of open quantum systems [1,2,3,4]
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 algorithm
A better understanding of dissipation in open quantum systems is a fundamental goal of quantum thermodynamics as well as being crucial for quantum device engineering
Summary
The importance of heat management at the nanoscale has grown in tandem with advances in the fabrication and control of small devices, motivating increasing interest in the nonequilibrium thermodynamics of open quantum systems [1,2,3,4]. A direct evaluation of the corresponding path integral is only possible for a few exactly solvable models, while numerical approaches based on the quasiadiabatic path-integral (QUAPI) method [52,53] require careful fine tuning to avoid error accumulation [54,55] We solve this problem by generalizing the time-evolving matrix product operator (TEMPO) algorithm [56] to calculate the characteristic function of energy changes in the bath, equivalent to the Fourier transform of the heat probability distribution. Our results show that the systembath interaction energy makes a considerable contribution to the heat statistics, even in the weak-coupling and hightemperature regime where a Markovian description of the system dynamics alone is accurate This underlines the need to interpret with great care the standard Markovian description of quantum thermodynamics [65], which is based on properties of the open system alone.
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