确定性无序介质中均匀N粒子安德森局域化和单峰本征态
Uniform N-particle Anderson localization and unimodal eigenstates in deterministic disordered media without induction on the number of particles
摘要：
本文首次给出了量子粒子相互作用系统的安德森局域化的严格结果，几乎周期性的）无序的外部电势。对于一类特定的确定性，费米子，安德森型哈密顿的任意维的晶格上，并为一个大类的底层动力系统产生的外部潜在的，我们证明了频谱是纯点，所有的本征态是单峰和功能的均匀指数衰减。与以前所有关于多粒子安德森局域化的数学工作不同，我们没有使用关于粒子数的归纳。
英文摘要：
We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic, Anderson-type Hamiltonians on the lattice of an arbitrary dimension, and for a large class of underlying dynamical systems generating the external potential, we prove that the spectrum is pure point, all eigenstates are unimodal and feature a uniform exponential decay. In contrast to all prior mathematical works on multi-particle Anderson localization, we do not use the induction on the number of particles.
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