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Asymptotic expansion of low-energy excitations for weakly interacting bosons

Part of: General mathematical topics and methods in quantum theory

Published online by Cambridge University Press:  26 March 2021

Lea Boßmann Open the ORCID record for Lea Boßmann [Opens in a new window] ,
Sören Petrat Open the ORCID record for Sören Petrat [Opens in a new window]  and
Robert Seiringer Open the ORCID record for Robert Seiringer [Opens in a new window]
Lea Boßmann
Affiliation:
Institute of Science and Technology Austria, Am Campus 1, 3400Klosterneuburg, Austria; E-mail: lea.bossmann@ist.ac.at.
Sören Petrat
Affiliation:
Department of Mathematics and Logistics, Jacobs University Bremen, Campus Ring 1, 28759Bremen, Germany; E-mail: s.petrat@jacobs-university.de. University of Bremen, Department 3 – Mathematics, Bibliothekstr. 5, 28359Bremen, Germany.
Robert Seiringer
Affiliation:
Institute of Science and Technology Austria, Am Campus 1, 3400Klosterneuburg, Austria; E-mail: robert.seiringer@ist.ac.at.

Abstract

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We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in $1/N$.

MSC classification

Secondary: 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis
Type
Mathematical Physics
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e28
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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