TY  - THES
A1  - Gogolin, Christian
T1  - Pure State Quantum Statistical Mechanics
T1  - Statistische Quantenmechanik mit reinen
Zuständen
N2  - The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement and uncertainty relations. No additional randomness is added by hand and no assumptions about a priori probabilities are made, instead measure concentration results are used to justify the methods of Statistical Physics. The approach explains the applicability of the microcanonical and canonical ensemble and the tendency to equilibrate in a natural way. This work contains a pedagogical review of the existing literature and some new results. The most important of which are: i) A measure theoretic justification for the microcanonical ensemble. ii) Bounds on the subsystem equilibration time. iii) A proof that a generic weak interaction causes decoherence in the energy eigenbasis. iv) A proof of a quantum H-Theorem. v) New estimates of the average effective dimension for initial product states and states from the mean energy ensemble. vi) A proof that time and ensemble averages of observables are typically close to each other. vii) A bound on the fluctuations of the purity of a system coupled to a bath.
N2  - Es wird ein neuer Ansatz die Methoden der Statistischen Physik aus der Quan- tenmechanik heraus zu rechtfertigen untersucht. Der gewählte Zugang ist echt quantenmechanisch. Statistisches Verhalten wird allein durch objektive quanten- mechanische Zufälligkeit auf Grund von Verschränkung und Unbestimmtheitsre- lationen erklärt. Es werden keine Annahmen über subjective Unwissenheit oder a priori Wahrscheinlichkeiten gemacht. Der Ansatz ist in der Lage eine maß- theoretische Rechtfertigung für die Anwendbarkeit des mikrokanonischen und des kanonischen Ensembles zu geben und erklärt auf natürliche Weise das Streben ins Gleichgewicht.
Diese Arbeit enthält einen Überblick über die vorhandene Literatur und eine Reihe von neuen Resultaten. Die wichtigsten neuen Ergebnisse sind: i) Eine maßtheoretische Begründung für die Anwendbarkeit des mikrokanonischen En- sembles. ii) Schranken für die Zeit bis ins Gleichgewicht.  iii) Aufzeigen eines generischen Dekohärenz-Mechanismus in der lokalen Energie-Eigenbasis bei schwa- cher Kopplung. iv) Beweis eines quantenmechanischen H-Theorems. v) Neue Abschätzungen der mittleren effektiven Dimension für Produktzustände und im “mittlere Energie”-Ensemble. vi) Ein Beweis, dass Zeit und Ensemblemittel typ- ischerweise nahezu zusammenfallen. vii) Eine Schranke für die Fluktuationen der Reinheit eines an ein Bad gekoppelten Systems.
KW  - Quantum Mechanics
KW  - Statistical Physics
KW  - Quantenstatistik
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-106065
ER  - 
TY  - JOUR
A1  - Janotta, Peter
A1  - Gogolin, Christian
A1  - Barrett, Jonathan
A1  - Brunner, Nicolas
T1  - Limits on nonlocal correlations from the structure of the local state space
N2  - The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson’s bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations—in particular whether the maximally entangled state violates Tsirelson’s bound or not— depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories—including, by extension, all bipartite classical and quantum states— cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.
KW  - Physik
Y1  - 2011
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-75003
ER  -