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14 - Quantum Statistical Mechanics

Published online by Cambridge University Press:  14 July 2022

Pierre Gaspard
Affiliation:
Université Libre de Bruxelles
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Summary

The overview of the principles of quantum statistical mechanics are given, emphasizing the fundamental differences with respect to classical statistical mechanics, as well as the analogies prevailing for the formulation of the properties. A functional time-reversal symmetry relation is presented, allowing the deduction of response theory. The Kubo formula is obtained for the linear response properties and the fluctuation–dissipation theorem is established. For weakly coupled systems, the quantum master equation and the corresponding stochastic Schrödinger equation are deduced. The slippage of initial conditions is discussed in relation to the positivity of the reduced statistical operator. The results are illustrated with the spin-boson model.

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Publisher: Cambridge University Press
Print publication year: 2022

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  • Quantum Statistical Mechanics
  • Pierre Gaspard, Université Libre de Bruxelles
  • Book: The Statistical Mechanics of Irreversible Phenomena
  • Online publication: 14 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108563055.015
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  • Quantum Statistical Mechanics
  • Pierre Gaspard, Université Libre de Bruxelles
  • Book: The Statistical Mechanics of Irreversible Phenomena
  • Online publication: 14 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108563055.015
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Quantum Statistical Mechanics
  • Pierre Gaspard, Université Libre de Bruxelles
  • Book: The Statistical Mechanics of Irreversible Phenomena
  • Online publication: 14 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108563055.015
Available formats
×