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Theory of elementary excitations in unstable Bose-Einstein condensates

U. Leonhardt·T. Kiss·P. Ohberg
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Abstract

Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the non-condensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to a sonic white hole and find that the spectrum of unstable modes is intrinsically discrete.

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U. Leonhardt, T. Kiss, P. Ohberg. 2002-11-21. Theory of elementary excitations in unstable Bose-Einstein condensates. https://arxiv.org/abs/cond-mat/0211462

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