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Equilibration and thermalization in quantum systems
Gogolin, Christian

HaupttitelEquilibration and thermalization in quantum systems
TitelvarianteEquilibrierung und Thermalisierung in Quantensystemen
AutorGogolin, Christian
Geburtsort: Karlsruhe
GutachterProf. Dr. Jens Eisert
weitere GutachterProf. Dr. Felix von Oppen
Freie Schlagwörterquantum mechanics; statistical mechanics; foundations; equilibration; thermalization
DDC530 Physik
ZusammenfassungThis thesis fathoms out the capabilities of the theory of quantum mechanics to explain thermodynamic behavior. It covers in particular equilibration and thermalization in closed quantum systems, typicality, time scales for equilibration, quantum integrability and its connection to thermalization, decoherence, and a maximum entropy principle. Together, the presented results form the body of the theory of pure state quantum statistical mechanics. With almost 300 references, ranging from the groundbreaking works of the early 20th century to the most recent discoveries (up to 2013), this work arguably constitutes the most comprehensive review of the literature on equilibration and thermalization in closed quantum systems. All results are presented in a unified notation and many are slightly strengthened or generalized.
Inhaltsverzeichnis1 Remarks on the foundations of statistical mechanics
1.1 Canonical approaches
1.1.1 Boltzmann and the H-Theorem
1.1.2 Gibbs' ensemble approach
1.1.3 (Quasi-)ergodicity
1.1.4 Jaynes' maximum entropy approach
1.2 Closing remarks
2 Pure state quantum statistical mechanics
2.1 Preliminaries and notation
2.1.1 Hilbert space and state vectors
2.1.2 Observables and states
2.1.3 Measurements and completely positive maps
2.1.4 Norms, distance measures and distinguishability
2.1.5 Entropy
2.1.6 Time evolution
2.1.7 Time averages and dephasing
2.1.8 Composite quantum systems and reduced states
2.1.9 Correlations and entanglement
2.1.10 Gibbs states
2.1.11 Microcanonical states
2.2 Equilibration
2.2.1 Notions of equilibration
2.2.2 Equilibration on average
2.2.3 Equilibration during intervals
2.2.4 A conjecture concerning equilibration
2.2.5 Other notions of equilibration
2.3 A quantum maximum entropy principle
2.4 Decoherence
2.5 Typicality
2.6 Time scales for equilibration on average
2.7 Thermalization
2.7.1 What is thermalization?
2.7.2 Thermalization under assumptions on the eigenstates
2.7.3 Thermalization under assumptions on the initial state
2.7.4 Hybrid approaches and other notions of thermalization
2.8 Absence of thermalization
2.8.1 Violation of subsystem initial state independence
2.8.2 A numerical investigation of the violation of initial state independence
2.9 Integrability
2.9.1 In classical mechanics
2.9.2 In quantum mechanics
2.10 Decay of correlations and stability of thermal states
3 Conclusions
Bibliography
A Back matter
A.1 Acknowledgements
A.2 Abstract
A.3 Zusammenfassung
A.4 Eigenständigkeitserklärung
A.5 Liste der Publikationen des Verfassers
A.6 Lebenslauf
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SeitenzahlVIII, 172 S.
Fachbereich/EinrichtungFB Physik
Erscheinungsjahr2014
Dokumententyp/-SammlungenDissertation
Medientyp/FormatText
SpracheEnglisch
RechteCreative Commons Lizenzvertrag
Equilibration and thermalization in quantum systems von Christian Gogolin ist lizenziert unter einer Creative Commons Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International Lizenz.
Anmerkungen des AutorsGefördert durch die Studienstiftung des deutschen Volkes
Tag der Disputation11.07.2014
Erstellt am15.07.2014 - 09:06:48
Letzte Änderung16.07.2014 - 12:15:53
 
Statische URLhttp://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000097097
URNurn:nbn:de:kobv:188-fudissthesis000000097097-7
Zugriffsstatistik