FEW BODY PROBLEM IN NANOCRYSTALS

我们从理论上研究了纳米晶体中电子-空穴系统的量子力学状态和动力学。主要结果如下：(1)我们建立了一种计算球形量子点中电子-空穴对态所有本征态的有效方法。这允许计算每个总角动量的本征态，并成为研究对任意微扰响应的数值方法的基础。(2)用我们的理论分析了嵌入在氯化钠晶体中的CuCl2纳米晶体的暂态吸收实验数据和双光子吸收光谱。(3)结合实际材料中观察到的持续空穴燃烧现象，研究了量子点外点电荷的影响。(4)通过数值计算研究了限制在球形量子点表面的电子-空穴对的本征态。并阐明了均匀磁场对量子隧穿的影响。(5)用一个简单的两粒子束缚态模型研究了复合粒子的量子隧穿。研究发现，即使在单势垒的情况下，也可能发生共振隧穿。

We have investigated theoretically quantum mechanical states and dynamics of electron-hole systems confined in nanocrystals. The main results are as follows.(1) We have established an efficient method to calculate essentially all of the eigenstates of an electron-hole pair state confined in spherical quantum dots. This allows for calculation of eigenstates of every total angular momentum, and becomes a basis of numerical method to investigate responses to arbitrary perturbations.(2) The experimental data of transient absorption and the 2-phohton absorption spectra obtained for CuCl nanocrystals embedded in NaCl crystals are analyzed by our theory. Good agreements between the measurements and the theoretical calculations are obtained.(3) The effects of a point charge located outside of quantum dots are investigated in connection with the persistent hole burnings observed in real materials.(4) The eigenstates of an electron-hole pair confined to a surface of spherical quantum dots are investigated by numerical calculation. The effects of a uniform magnetic field are also clarified.(5) Quantum tunneling of a composite particle is investigated by a simple two-particle bound state model. It is found that resonant tunneling may occur even in the case of a single potential barrier.