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Collective behaviours of weakly interacting Bose gases III

Phan Thanh Nam
IST Vienna
Thursday, February 16, 2017 - 16:15 to 18:00

This mini-course discusses rigorous results of bosonic systems when the number of particles is large and the interaction between particles is sufficiently weak. Starting from the first principles of quantum mechanics, namely from Schroedinger's equation for many-body systems, we will show that many collective properties of the systems can be described by effective mean-field models: Gross-Pitaevskii theory (leading order) and Bogoliubov theory (second order). 

1. Gross-Pitaevskii theory  
- Bose-Einstein condensation and Gross-Pitaevskii theory
- Quantum de Finetti theorem
- Justification of Gross-Pitaevskii theory for trapped systems
2. Bogoliubov theory: 
- Excited particles and Bogoliubov theory
- Operator inequalities in Fock space
- Justification of Bogoliubov theory for excitation spectrum
- Justification of Bogoliubov theory for quantum dynamics

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