EAGER: Quantum Nanosystems Understood the Multiscale Way

为了理解量子纳米系统，开发了一种数学和计算方法，该方法利用了平均最近邻距离和整个系统大小之间的尺度分离。推导方法从N-费米子波动方程出发，得到纳纳秒尺度激发的粗粒度方程。粗粒度波动方程给出了描述纳米尺度特征的序参数的量子动力学。考虑了几种类型的有序参数(例如，标度粒子位置、整个系统形变和自旋/数密度分布)。该理论基于一个假设，即波函数直接或间接地通过一组序参数与N粒子构型有多个依赖关系。其结果是一个严格的算法来模拟量子纳米系统的长时空尺度动力学。应用的例子有量子点、石墨烯薄片和纳米带。该项目对大分子组装、量子点、类石墨烯结构和其他量子纳米系统的量子行为理论产生了影响。该项目产生的理论、算法和软件对纳米级量子器件的计算机辅助设计、超导纳米结构和其他异常电路元件的设计产生了影响。与Prairie View A&amp；M大学的合作，通过跨越学年和夏季的几项教育活动，吸引了两所大学中代表性不足的群体，包括学生和教职员工。这个热切的项目得到了一个联合奖项的支持，该奖项包括化学部(理论、模型和计算方法以及高分子、超分子和纳米化学)和数学科学部(应用数学项目)的两个项目。

Mathematical and computational methods for understanding quantum nanosystems are developed based on a methodology that takes advantage of the separation of scales between the average nearest-neighbor distance and the overall system size. The deductive methodology starts with the N-fermion wave equation and results in coarse-grained equations for nanometer-nanosecond scale excitations. The coarse-grained wave equations yield the quantum dynamics of order parameters describing nanoscale features. Several types of order parameters (e.g., scaled particle positions, overall system deformation, and spin/number density profiles) are considered. The theory is based on a hypothesis that the wave function has multiple dependencies on the N-particle configuration, directly and indirectly via a set of order parameters. The result is a rigorous algorithm for simulating the long space-time scale dynamics of quantum nanosystems. Examples of applications are quantum dots, graphene flakes and nanoribbons. The project has impact on the theory of the quantum behavior of macromolecular assemblies, quantum dots, graphene-like structures, and other quantum nanosystems. Theory, algorithms, and software resulting from this project have impact on the computer-aided design of nanoscale quantum devices, the designing of superconducting nanostructures and other anomalous circuit elements. Collaboration with Prairie View A & M University engages underrepresented groups, both students and faculty, in the two institutions via several educational activities spanning the academic year and the summer. This EAGER project is supported by a joint award including two programs in the Chemistry Division (Theory, Models and Computational Methods and Macromolecular, Supramolecular and Nanochemistry) and the Division of Mathematical Sciences (Applied Mathematics program).