Abstract:In this paper we investigate the effect of repulsive pair interactions on Bose–Einstein condensation in a well-established random one-dimensional system known as the Luttinger–Sy model at positive temperature. We study separately hard core interactions as well as a class of more general repulsive interactions, also allowing for a scaling of certain interaction parameters in the thermodynamic limit. As a main result, we prove in both cases that for sufficiently strong interactions all eigenstates of the non-interacting one-particle Luttinger–Sy Hamiltonian are $\mathbb {P}$-almost surely not macroscopically occupied. We also outline an extension of the results to sufficiently localized one-particle states.

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中文翻译：

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Luttinger-Sy 模型中排斥对相互作用对 Bose-Einstein 凝聚的影响

摘要：在本文中，我们研究了斥力对相互作用对正温度下一个完善的随机一维系统（称为 Luttinger-Sy 模型）中 Bose-Einstein 凝聚的影响。我们分别研究硬核相互作用以及一类更一般的排斥相互作用，还允许在热力学极限中缩放某些相互作用参数。作为主要结果，我们在这两种情况下证明，对于足够强的相互作用，非相互作用的单粒子 Luttinger-Sy 哈密顿量的所有本征态都是 $\mathbb {P}$-几乎肯定不会被宏观占用。我们还概述了将结果扩展到足够局部化的单粒子状态。

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