The BBGKY hierarchy for ultracold bosonic systems: II. Applications

TL;DR

This paper applies the truncated BBGKY hierarchy to ultracold bosonic systems in out-of-equilibrium scenarios, analyzing its accuracy, instabilities, and stabilization methods for different interaction strengths and timescales.

Contribution

It demonstrates the application of a previously developed theoretical framework to specific dynamical scenarios, exploring the impact of truncation order and stability corrections.

Findings

Short-time dynamics are accurately described.

Long-time deviations occur with strong interactions.

Minimal-invasive correction stabilizes the hierarchy.

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.