Scattering induced current in a tight-binding band

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.

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。

紧束缚模型在谱退化点附近的大尺度近似及波包传播的有效性

Macroscopic approximation of tight-binding models near spectral degeneracies and validity for wave packet propagation

本文研究了紧束缚模型在谱退化点附近波包的宏观近似及其在石墨烯哈密顿量中的有效性，通过数值模拟验证了宏观模型的长期准确性。

Point Defects in Tight Binding Models for Insulators

We consider atomistic geometry relaxation in the context of linear tight binding models for point defects. A limiting model as Fermi-temperature is sent to zero is formulated, and an exponential rate of convergence for the nuclei configuration is established. We also formulate the thermodynamic limit model at zero Fermi-temperature, extending the results of [H. Chen, J. Lu, C. Ortner. Arch. Ration. Mech. Anal., 2018]. We discuss the non-trivial relationship between taking zero temperature and thermodynamic limits in the finite Fermi-temperature models.