Point Defects in Tight Binding Models for Insulators

Locality of Interatomic Interactions in Self-Consistent Tight Binding Models

A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability condition, we construct such a spatial decomposition for self-consistent tight binding models, extending recent results for linear tight binding models to the non-linear setting.

Locality of Interatomic Forces in Tight Binding Models for Insulators

The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed into exponentially localised site energy contributions, thus providing qualitatively sharp estimates on the interatomic interaction range which justifies a range of multi-scale models. For insulators at finite Fermi-temperature we obtain locality estimates that are uniform in the zero-temperature limit. A particular feature of all our results is that they depe…

Scattering induced current in a tight-binding band

In the single band tight-binding approximation, we consider the transport properties of an electron in a homogeneous static electric field. We show that repeated interactions of the electron with two-level systems in thermal equilibrium suppress the Bloch oscillations and induce a steady current, the statistical properties of which we study.

Decorrelation estimates for a 1D tight binding model in the localized regime

In this article, we prove decorrelation estimates for the eigenvalues of a 1D discrete tight binding model near two distinct energies in the localized regime. Consequently, with an arbitrary, fixed number n, the asymptotic independence for local level statistics near n distinct energies is obtained.

两粒子Anderson紧束缚模型的本征函数

Eigenfunctions in a two-particle Anderson tight binding model

我们建立了一个具有短程相互作用的d维晶格上的量子两粒子系统的Anderson局域化现象，并且存在一个具有足够规则的边缘分布的IID外部势。

两粒子紧束缚模型的Wegner界

Wegner bounds for a two-particle tight binding model

考虑了具有相互作用和IID外部势的d维晶格上的量子两粒子系统。我们建立这样一个模型的Wegner型估计。使用的主要工具是Stollmann引理。