Equilibration and thermalization in quantum systems

摘要: 1 Remarks on the foundations of statistical mechanics 1.1 Canonical approaches 1.1.1 Boltzmann and H-Theorem 1.1.2 Gibbs' ensemble approach 1.1.3 (Quasi-)ergodicity 1.1.4 Jaynes' maximum entropy 1.2 Closing remarks 2 Pure state quantum 2.1 Preliminaries notation 2.1.1 Hilbert space vectors 2.1.2 Observables states 2.1.3 Measurements completely positive maps 2.1.4 Norms, distance measures and distinguishability 2.1.5 Entropy 2.1.6 Time evolution 2.1.7 averages and dephasing 2.1.8 Composite systems reduced 2.1.9 Correlations entanglement 2.1.10 Gibbs 2.1.11 Microcanonical states 2.2 Equilibration 2.2.1 Notions equilibration 2.2.2 on average 2.2.3 during intervals 2.2.4 A conjecture concerning equilibration 2.2.5 Other notions 2.3 maximum entropy principle 2.4 Decoherence 2.5 Typicality 2.6 scales for equilibration average 2.7 Thermalization 2.7.1 What is thermalization? 2.7.2 under assumptions eigenstates 2.7.3 Thermalization under initial 2.7.4 Hybrid approaches other notions thermalization 2.8 Absence 2.8.1 Violation of subsystem independence 2.8.2 numerical investigation the violation 2.9 Integrability 2.9.1 In classical mechanics 2.9.2 2.10 Decay correlations stability of thermal 3 Conclusions Bibliography Back matter A.1 Acknowledgements A.2 Abstract A.3 Zusammenfassung A.4 Eigenstandigkeitserklarung A.5 Liste der Publikationen des Verfassers A.6 Lebenslauf