A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates

M. Kreibich; H. Cartarius; J. Main; G. Wunner

doi:10.1063/1.4745583

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arXiv · 1206.0920

A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates

M. Kreibich·H. Cartarius·J. Main·G. Wunner

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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.

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M. Kreibich, H. Cartarius, J. Main, G. Wunner. 2012-06-05. A nonlinear dynamics approach to Bogoliubov excitations of Bose-Einstein condensates. https://doi.org/10.1063/1.4745583

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