Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Thermodynamics
- 2 Statistical Mechanics
- 3 Hydrodynamics
- 4 Stochastic Processes
- 5 Fluctuation Relations for Energy and Particle Fluxes
- 6 Path Probabilities, Temporal Disorder, and Irreversibility
- 7 Driven Brownian Particles and Related Systems
- 8 Effusion Processes
- 9 Processes in Dilute and Rarefied Gases
- 10 Fluctuating Chemohydrodynamics
- 11 Reactions
- 12 Active Processes
- 13 Transport in Hamiltonian Dynamical Models
- 14 Quantum Statistical Mechanics
- 15 Transport in Open Quantum Systems
- Appendix A Complements on Thermodynamics
- Appendix B Complements on Dynamical Systems Theory
- Appendix C Complements on Statistical Mechanics
- Appendix D Complements on Hydrodynamics
- Appendix E Complements on Stochastic Processes
- Appendix F Complements on Fluctuation Relations
- References
- Index
14 - Quantum Statistical Mechanics
Published online by Cambridge University Press: 14 July 2022
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Thermodynamics
- 2 Statistical Mechanics
- 3 Hydrodynamics
- 4 Stochastic Processes
- 5 Fluctuation Relations for Energy and Particle Fluxes
- 6 Path Probabilities, Temporal Disorder, and Irreversibility
- 7 Driven Brownian Particles and Related Systems
- 8 Effusion Processes
- 9 Processes in Dilute and Rarefied Gases
- 10 Fluctuating Chemohydrodynamics
- 11 Reactions
- 12 Active Processes
- 13 Transport in Hamiltonian Dynamical Models
- 14 Quantum Statistical Mechanics
- 15 Transport in Open Quantum Systems
- Appendix A Complements on Thermodynamics
- Appendix B Complements on Dynamical Systems Theory
- Appendix C Complements on Statistical Mechanics
- Appendix D Complements on Hydrodynamics
- Appendix E Complements on Stochastic Processes
- Appendix F Complements on Fluctuation Relations
- References
- Index
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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- The Statistical Mechanics of Irreversible Phenomena , pp. 494 - 519Publisher: Cambridge University PressPrint publication year: 2022