We assume the macroscopic wave function of a Bose-Einstein condensate as a superposition of Gaussian wave packets, with time-dependent complex width parameters, insert it into the mean-field energy functional corresponding to the Gross-Pitaevskii equation (GPE) and apply the time-dependent variational principle. In this way the GPE is mapped onto a system of coupled equations of motion for the complex width parameters, which can be analyzed using the methods of nonlinear dynamics. We perform a stability analysis of the fixed points of the nonlinear system, and demonstrate that the eigenvalues of the Jacobian reproduce the low-lying quantum mechanical Bogoliubov excitation spectrum of a condensate in an axisymmetric trap.
Description
A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates: AIP Conference Proceedings: Vol 1468, No 1
%0 Journal Article
%1 kreibich2012nonlinear
%A Kreibich, M
%A Cartarius, H
%A Main, J
%A Wunner, G
%B AIP Conference Proceedings
%D 2012
%I American Institute of Physics
%J AIP Conference Proceedings
%K main_itp1
%N 1
%P 216--222
%R 10.1063/1.4745583
%T A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates
%U https://aip.scitation.org/doi/abs/10.1063/1.4745583
%V 1468
%X We assume the macroscopic wave function of a Bose-Einstein condensate as a superposition of Gaussian wave packets, with time-dependent complex width parameters, insert it into the mean-field energy functional corresponding to the Gross-Pitaevskii equation (GPE) and apply the time-dependent variational principle. In this way the GPE is mapped onto a system of coupled equations of motion for the complex width parameters, which can be analyzed using the methods of nonlinear dynamics. We perform a stability analysis of the fixed points of the nonlinear system, and demonstrate that the eigenvalues of the Jacobian reproduce the low-lying quantum mechanical Bogoliubov excitation spectrum of a condensate in an axisymmetric trap.
@article{kreibich2012nonlinear,
abstract = {We assume the macroscopic wave function of a Bose-Einstein condensate as a superposition of Gaussian wave packets, with time-dependent complex width parameters, insert it into the mean-field energy functional corresponding to the Gross-Pitaevskii equation (GPE) and apply the time-dependent variational principle. In this way the GPE is mapped onto a system of coupled equations of motion for the complex width parameters, which can be analyzed using the methods of nonlinear dynamics. We perform a stability analysis of the fixed points of the nonlinear system, and demonstrate that the eigenvalues of the Jacobian reproduce the low-lying quantum mechanical Bogoliubov excitation spectrum of a condensate in an axisymmetric trap.},
added-at = {2018-12-04T23:35:55.000+0100},
author = {Kreibich, M and Cartarius, H and Main, J and Wunner, G},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2e41a245ace5e77558a781919713b5e1f/rbardak},
booktitle = {AIP Conference Proceedings},
comment = {doi: 10.1063/1.4745583},
description = {A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates: AIP Conference Proceedings: Vol 1468, No 1},
doi = {10.1063/1.4745583},
interhash = {b7b6842f77adb2130e1d7166da681f5b},
intrahash = {e41a245ace5e77558a781919713b5e1f},
issn = {0094243X},
journal = {AIP Conference Proceedings},
keywords = {main_itp1},
month = aug,
number = 1,
pages = {216--222},
publisher = {American Institute of Physics},
timestamp = {2018-12-04T22:35:55.000+0100},
title = {A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates},
url = {https://aip.scitation.org/doi/abs/10.1063/1.4745583},
volume = 1468,
year = 2012
}
