Collective excitations of Bose gases in the mean-field regime

P. Nam, R. Seiringer, Archive for Rational Mechanics and Analysis 215 (2015) 381–417.


Journal Article | Published | English
Department
Abstract
We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer.
Publishing Year
Date Published
2015-02-01
Journal Title
Archive for Rational Mechanics and Analysis
Volume
215
Issue
2
Page
381 - 417
IST-REx-ID

Cite this

Nam P, Seiringer R. Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. 2015;215(2):381-417. doi:10.1007/s00205-014-0781-6
Nam, P., & Seiringer, R. (2015). Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis, 215(2), 381–417. https://doi.org/10.1007/s00205-014-0781-6
Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” Archive for Rational Mechanics and Analysis 215, no. 2 (2015): 381–417. https://doi.org/10.1007/s00205-014-0781-6.
P. Nam and R. Seiringer, “Collective excitations of Bose gases in the mean-field regime,” Archive for Rational Mechanics and Analysis, vol. 215, no. 2, pp. 381–417, 2015.
Nam P, Seiringer R. 2015. Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. 215(2), 381–417.
Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” Archive for Rational Mechanics and Analysis, vol. 215, no. 2, Springer, 2015, pp. 381–417, doi:10.1007/s00205-014-0781-6.

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