The Excitation Spectrum for Bose Fluids with Weak Interactions

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Abstract

We review recent progress towards a rigorous understanding of the excitation spectrum of bosonic quantum many-body systems. In particular, we explain how one can rigorously establish the predictions resulting from the Bogoliubov approximation in the mean field limit. The latter predicts that the spectrum is made up of elementary excitations, whose energy behaves linearly in the momentum for small momentum. This property is crucial for the superfluid behavior of the system. We also discuss a list of open problems in this field.

Keywords

Schrödinger equation Quantum statistical mechanics Bose–Einstein condensation Dilute Bose gas Superfluidity Excitation spectrum 

Mathematics Subject Classification

82B10 82-02 46N50 

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Copyright information

© The Author 2014. Published by Springer-Verlag GmbH Berlin Heidelberg in cooperation with the Deutsche Mathematiker-Vereinigung. All rights reserved. 2014

Authors and Affiliations

  1. 1.IST AustriaKlosterneuburgAustria

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