The Excitation Spectrum for Weakly Interacting Bosons

By Robert Seiringer. 2010

158 citations recorded by the source corpus.

We investigate the low energy excitation spectrum of a Bose gas with weak, long range repulsive interactions. In particular, we prove that the Bogoliubov spectrum of elementary excitations with linear dispersion relation for small momentum becomes exact in the mean-field limit.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/528df16ba3cc2909e822061d674dad65329f1ffd

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Mathematical Physics

Citations in the corpus

Mean–Field Evolution of Fermionic Systems (2013, background): “A first proof of the emergence of Bogoliubov excitation spectrum has been found in [38] (for systems of bosons in a box) and in [24] (in the presence of an external potential).”
Derivation of Hartree's theory for generic mean-field Bose systems (2013, methodology): “3) is available in the literature for numerous special cases, including “bosonic atoms” [9, 62, 5, 6, 33], boson stars [45, 46], the homogeneous Bose gas [56], trapped Bose gases [27], the Lieb-Liniger model [40, 57], and many others.”
Bogoliubov Spectrum of Interacting Bose Gases (2012, methodology): “In [53, 24], Seiringer and Grech have shown a result similar to Theorem 2.”
The Excitation Spectrum for Weakly Interacting Bosons in a Trap (2012, methodology): “It is instructive to compare Theorem 1 with the translation invariant case studied in [24], where the Bose gas is confined to the flat unit torus Td.”