Quantum heat statistics with time-evolving matrix product operators

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

doi:10.1103/PRXQuantum.2.020338

Quantum heat statistics with time-evolving matrix product operators

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

School of Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	020338
Number of pages	18
Journal	PRX Quantum
Volume	2
Issue number	2
DOIs	https://doi.org/10.1103/PRXQuantum.2.020338
Publication status	Published - 10 Jun 2021

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Popovic-2021-Quantum-heat-statistics-PRXQ-2-020338-CCBY
Copyright © 2021 the Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
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Understanding and engineering: Understanding and engineering dissipation in nanoscale quantum devices
Lovett, B. W. (PI) & Keeling, J. M. J. (CoI)
EPSRC
1/04/20 → 31/03/23
Project: Standard

Quantum heat statistics with time-evolving matrix product operators (associated code)
Popovic, M. (Creator), Mitchison, M. T. (Creator), Strathearn, A. (Creator), Lovett, B. W. (Creator), Goold, J. (Creator) & Eastham, P. R. (Creator), Zenodo, 2021
DOI: 10.5281/zenodo.4884728
Dataset

Cite this

@article{9f60b455dcb44754875d1f9f51e57c37,

title = "Quantum heat statistics with time-evolving matrix product operators",

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. ",

author = "Maria Popovic and Mark Mitchison and Aidan Strathearn and Lovett, {Brendon W.} and John Goold and Paul Eastham",

note = "Funding: We acknowledge funding from the European Research Council under the European Union{\textquoteright}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).",

year = "2021",

month = jun,

day = "10",

doi = "10.1103/PRXQuantum.2.020338",

language = "English",

volume = "2",

journal = "PRX Quantum",

issn = "2691-3399",

publisher = "American Physical Society",

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TY - JOUR

T1 - Quantum heat statistics with time-evolving matrix product operators

AU - Popovic, Maria

AU - Mitchison, Mark

AU - Strathearn, Aidan

AU - Lovett, Brendon W.

AU - Goold, John

AU - Eastham, Paul

N1 - Funding: 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).

PY - 2021/6/10

Y1 - 2021/6/10

N2 - 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.

AB - 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.

U2 - 10.1103/PRXQuantum.2.020338

DO - 10.1103/PRXQuantum.2.020338

M3 - Article

SN - 2691-3399

VL - 2

JO - PRX Quantum

JF - PRX Quantum

IS - 2

M1 - 020338

ER -

Quantum heat statistics with time-evolving matrix product operators

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Understanding and engineering: Understanding and engineering dissipation in nanoscale quantum devices

Datasets

Quantum heat statistics with time-evolving matrix product operators (associated code)

Cite this