dc.contributor.author
Gogolin, Christian
dc.date.accessioned
2018-06-08T01:06:39Z
dc.date.available
2014-07-16T12:15:53.853Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/12943
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-17141
dc.description
1 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
dc.description.abstract
This 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.
de
dc.description.abstract
Diese Arbeit lotet aus, inwieweit thermodynamisches Verhalten auf der Basis
von Quantenmechanik erklärt werden kann. Behandelt werden insbesondere:
Equilibrierung und Thermalisierung in abgeschlossenen Quantensystemen,
Typikalität, die Zeitskalen auf denen Equilibrierung stattfindet,
Integrabilität in der Quantenmechanik, Dekoherenz und ein Prinzip der
maximalen Entropie. Zusammengenommen bilden die präsentierten Resultate die
Theorie der ``pure state quantum statistical mechanics''. Mit fast 300
Referenzen aus allen Phasen der Entwicklung des Feldes, von den Anfängen im
frühen 20. Jahrhundert bis zu den jüngsten Ergebnissen (bis einschließlich
2013), gibt die Arbeit die bisher wohl umfassendste Übersicht zum Thema
Equilibrierung und Thermalisierung in geschlossenen Quantensystemen. Alle
Resultate werden in einer vereinheitlichten Notation präsentiert und viele
leicht verbessert oder verallgemeinert.
de
dc.format.extent
VIII, 172 S.
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject
quantum mechanics
dc.subject
statistical mechanics
dc.subject
thermalization
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik
dc.title
Equilibration and thermalization in quantum systems
dc.contributor.firstReferee
Prof. Dr. Jens Eisert
dc.contributor.furtherReferee
Prof. Dr. Felix von Oppen
dc.date.accepted
2014-07-11
dc.identifier.urn
urn:nbn:de:kobv:188-fudissthesis000000097097-7
dc.title.translated
Equilibrierung und Thermalisierung in Quantensystemen
en
refubium.affiliation
Physik
de
refubium.mycore.fudocsId
FUDISS_thesis_000000097097
refubium.note.author
Gefördert durch die Studienstiftung des deutschen Volkes
refubium.mycore.derivateId
FUDISS_derivate_000000015496
dcterms.accessRights.dnb
free
dcterms.accessRights.openaire
open access