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Norm Approximation for Many-Body Quantum Dynamics and Bogoliubov Theory

  • Phan Thành NamEmail author
  • Marcin Napiórkowski
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 18)

Abstract

We review some recent results on the norm approximation to the Schrödinger dynamics. We consider N bosons in \(\mathbb{R}^{3}\) with an interaction potential of the form N 3β−1 w(N β (xy)) with 0 ≤ β < 1∕2, and show that in the large N limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation.

Keywords

Bogoliubov approximation Bose-Einstein condensation Many body quantum dynamics 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic
  2. 2.Faculty of Physics, Department of Mathematical Methods in PhysicsUniversity of WarsawWarszawaPoland

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