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arXiv · 1712.00821

The BBGKY hierarchy for ultracold bosonic systems: II. Applications

Sven Krönke·Peter Schmelcher
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Abstract

In this work, which is based on our previously derived theoretical framework [1], we apply the truncated Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy for ultracold bosonic systems with a fixed number of particles to two out-of-equilibrium scenarios, namely tunneling in a double-well potential and an interaction quench in a harmonic trap. The efficient formulation of the theory provided in [1] allows for going to large truncation orders such that the impact of the truncation order on the accuracy of the results can be systematically explored. While the short-time dynamics is found to be excellently described with controllable accuracy, significant deviations occur on a longer time-scale for a sufficiently strong interaction quench or the tunneling scenario. Theses deviations are accompanied by exponential-like instabilities leading to unphysical results. The phenomenology of these instabilities is investigated in detail and we show that the minimal-invasive correction algorithm of the equation of motion as proposed in [1] can indeed stabilize the BBGKY hierarchy truncated at the second order.

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Sven Krönke, Peter Schmelcher. 2017-12-03. The BBGKY hierarchy for ultracold bosonic systems: II. Applications. https://doi.org/10.1103/physreva.98.013629

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