标题： Anderson局域化对于相互作用的双粒子量子系统在${\mathbb Z}$上的研究 显示英文标题

标题： Anderson localisation for an interacting two-particle quantum system on ${\mathbb Z}$

摘要： 我们研究了整数格点上具有有界短程两体相互作用的双量子粒子系统的谱性质，在一个外部随机势场$V(x,\omega)$中，其中随机变量具有独立且同分布的值。 主要结果是，如果随机变量$V(x,\omega)$的公共概率密度$f$在实轴附近的条带内是解析的，并且幅度常数$g$足够大（即系统处于高无序状态），那么以概率 1，双粒子晶格薛定谔算子$H(\omega)$（玻色子或费米子）的谱是纯点谱，并且所有本征函数都以指数衰减。本文中的证明基于对 von Dreifus 和 Klein 提出的多尺度分析（MSA）方案的一种改进，该方案经过调整以适用于具有相互作用的晶格系统。 显示英文摘要

摘要： We study spectral properties of a system of two quantum particles on an integer lattice with a bounded short-range two-body interaction, in an external random potential field $V(x,\omega)$ with independent, identically distributed values. The main result is that if the common probability density $f$ of random variables $V(x,\omega)$ is analytic in a strip around the real line and the amplitude constant $g$ is large enough (i.e. the system is at high disorder), then, with probability one, the spectrum of the two-particle lattice Schroedinger operator $H(\omega)$ (bosonic or fermionic) is pure point, and all eigen-functions decay exponentially. The proof given in this paper is based on a refinement of a multiscale analysis (MSA) scheme proposed by von Dreifus and Klein, adapted to incorporate lattice systems with interaction.