We study the multiparticle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multiparticle lower spectral edges are almost surely constant in absence of ergodicity. We stress that this result is not quite obvious and has to be handled carefully. In addition, we prove the spectral exponential and the strong dynamical localization of the continuous multiparticle Anderson model at low energy. The proof based on the multiparticle multiscale analysis bounds needs the values of the external random potential to be independent and identically distributed, whose common probability distribution is at least Log-Hölder continuous.

中文翻译：

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多维连续安德森模型的低能多粒子定位

我们研究了连续体中的多粒子安德森模型，并表明在对随机外部电势和粒子间相互作用的一些温和假设下，对于任何有限数量的粒子，在没有遍历性的情况下，多粒子下光谱边缘几乎可以确定地保持恒定。我们强调，这个结果不是很明显，必须谨慎处理。此外，我们证明了连续多粒子安德森模型在低能量下的光谱指数和强动力学局部性。基于多粒子多尺度分析边界的证明需要外部随机势的值独立且均匀分布，其共同概率分布至少为Log-Hölder连续。