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arXiv · 2004.05416

On the Schr\"odinger-Lohe hierarchy for aggregation and its emergent dynamics

Seung-Yeal Ha·Hansol Park
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Abstract

The Lohe hierarchy is a hierarchy of finite-dimensional aggregation models consisting of the Kuramoto model, the complex Lohe sphere model, the Lohe matrix model and the Lohe tensor model. In contrast, the Schr\"odinger-Lohe model is the only known infinite-dimensional Lohe aggregation model in literature. In this paper, we provide an explicit connection between the Schr\"odinger-Lohe model and the complex Lohe sphere model, and then by exploiting this explicit relation, we construct infinite-dimensional liftings of the Lohe matrix and the Lohe tensor models. In this way, we establish the Schr\"odinger-Lohe hierarchy which corresponds to the infinite-dimensional extensions of the Lohe hierarchy. For the proposed hierarchy, we provide sufficient frameworks leading to the complete aggregation in terms of coupling strengths and initial configurations.

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Seung-Yeal Ha, Hansol Park. 2020-04-11. On the Schr\"odinger-Lohe hierarchy for aggregation and its emergent dynamics. https://doi.org/10.1007/s10955-020-02659-0

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