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1 results

  • 14 - Quantum Statistical Mechanics

  • Pierre Gaspard, Université Libre de Bruxelles
  • Book:
    The Statistical Mechanics of Irreversible Phenomena
    Published online:
    14 July 2022
    Print publication:
    28 July 2022, pp 494-519

  • 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.