量子点氦的非线性Schroedinger-Poisson理论
Nonlinear Schroedinger-Poisson Theory for Quantum-Dot Helium
摘要：
我们用非线性薛定谔-泊松方程来描述两个自旋相反的相互作用的电子被限制在一个抛物势场中，一个量子点。考虑到二维电子系统和三维静电场的尺寸失配，我们提出了一种有效形式的泊松方程。结果与以前的数值计算在两体状态的大的基础上进行的，并提供了一个简单的模型，连续量子经典跃迁的非线性增加。由于本征态的非正交性的具体有趣的属性进行了强调。
英文摘要：
We use a nonlinear Schroedinger-Poisson equation to describe two interacting electrons with opposite spins confined in a parabolic potential, a quantum dot. We propose an effective form of the Poisson equation taking into account the dimensional mismatch of the two-dimensional electronic system and the three-dimensional electrostatics. The results agree with earlier numerical calculations performed in a large basis of two-body states and provide a simple model for continuous quantum-classical transition with increasing nonlinearity. Specific intriguing properties due to eigenstate non-orthogonality are emphasized.
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