caa a22 4500 605515387 CHVBK 20210128100709.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00205-014-0781-6 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0781-6 Collective Excitations of Bose Gases in the Mean-Field Regime [Elektronische Daten] [Phan Nam, Robert Seiringer] 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. Springer-Verlag Berlin Heidelberg, 2014 Nam Phan IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria aut Seiringer Robert IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/2(2015-02-01), 381-417 0003-9527 215:2<381 2015 215 205 https://doi.org/10.1007/s00205-014-0781-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0781-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nam Phan IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria aut NATIONALLICENCE 700 1- Seiringer Robert IST Austria, Am Campus 1, 3400, Klosterneuburg, Austria aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/2(2015-02-01), 381-417 0003-9527 215:2<381 2015 215 205