具有一般“粗糙”准周期势的两粒子晶格模型的Wegner型边界
Wegner-type bounds for a two-particle lattice model with a generic "rough" quasi-periodic potential
摘要：
本文考虑一类两粒子紧束缚哈密顿量，它描述了格点$\Z^d$，$d\ge 1$上相互作用的量子粒子对受一个共同的外势$V(x)$的作用，我们假设外势是准周期的，并且依赖于一个辅助参数.这种遍历确定性势的参数族（“大系综”）已经在\cite{C07}中在单粒子晶格系统的框架内引入，其中证明了Wegner界的非均匀模拟对一类准周期大系综成立。利用\cite{CS08}中提出的方法，我们建立了一类具有非随机短程相互作用的准周期两粒子晶格系统的体积相关Wegner型边界.
英文摘要：
In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice $\Z^d$, $d\ge 1$ subject to a common external potential $V(x)$ which we assume quasi-periodic and depending on an auxiliary parameter. Such parametric families of ergodic deterministic potentials ("grand ensembles") have been introduced earlier in \cite{C07}, in the framework of single-particle lattice systems, where it was proved that a non-uniform analog of the Wegner bound holds true for a class of quasi-periodic grand ensembles. Using the approach proposed in \cite{CS08}, we establish volume-dependent Wegner-type bounds for a class of quasi-periodic two-particle lattice systems with a non-random short-range interaction.
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