论文标题
量子纳米电子设备的大规模静电模拟的无轨道方法
Orbital-free approach for large-scale electrostatic simulations of quantum nanoelectronics devices
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
The route to reliable quantum nanoelectronic devices hinges on precise control of the electrostatic environment. For this reason, accurate methods for electrostatic simulations are essential in the design process. The most widespread methods for this purpose are the Thomas-Fermi approximation, which provides quick approximate results, and the Schrödinger-Poisson method, which better takes into account quantum mechanical effects. The mentioned methods suffer from relevant shortcomings: the Thomas-Fermi method fails to take into account quantum confinement effects that are crucial in heterostructures, while the Schrödinger-Poisson method suffers severe scalability problems. This paper outlines the application of an orbital-free approach inspired by density functional theory. By introducing gradient terms in the kinetic energy functional, our proposed method incorporates corrections to the electronic density due to quantum confinement while it preserves the scalability of a theory that can be expressed as a functional minimization problem. This method offers a new approach to addressing large-scale electrostatic simulations of quantum nanoelectronic devices.
