In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to bosonic systems with infinitely many degrees of freedom, we address the problem of persistence of fragmented condensation. We show that the latter occurs in interacting systems, in the mean-field regime, and in the limit of large gap of the one-body Hamiltonian.

中文翻译：

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关于碎片凝结的一些严格方面

在本文中，我们从数学的角度讨论了碎片凝聚的一些方面。我们首先提出了一种表征有限碎片的简单方法。然后，受最近应用于具有无限多自由度的玻色子系统的半经典分析结果的启发，我们解决了碎片凝聚的持久性问题。我们表明后者发生在相互作用的系统中，在平均场制度中，以及在单体哈密顿量的大间隙的极限中。