EAGER: Quantum Nanosystems Understood the Multiscale Way

EAGER：量子纳米系统了解多尺度方式

• 批准号: 1037383
• 负责人: Peter Ortoleva
• 金额: $ 24万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-15 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1037383&HistoricalAwards=false
• 关键词: EAGER; Quantum; Nanosystems; Understood; Multiscale

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).

用于理解量子纳米系统的数学和计算方法是基于一种方法来开发的，该方法利用了平均最近邻居距离和整体系统大小之间的尺度分离。演绎方法始于N-屈光度波方程，并为纳米纳秒刻度激发带来粗粒方程。粗粒波方程产生了描述纳米级特征的顺序参数的量子动力学。考虑了几种类型的订单参数（例如，缩放粒子位置，整体系统变形和自旋/数密度轮廓）。该理论基于一个假设，即波函数通过一组顺序参数直接和间接地对N粒子配置具有多个依赖性。结果是一种严格的算法，用于模拟量子纳米系统的长时间尺度动力学。应用的示例是量子点，石墨烯薄片和纳米容器。该项目对大分子组件，量子点，石墨烯状结构和其他量子纳米系统的量子行为的理论产生了影响。该项目产生的理论，算法和软件对纳米级量子设备的计算机辅助设计，超导纳米结构的设计和其他异常电路元素的设计。与Prairie View A＆M大学合作，通过跨越学年和夏季的几项教育活动，在这两个机构中与学生和教职员工的代表性不足。该急切的项目得到了联合奖项的支持，包括化学部门的两个计划（理论，模型和计算方法以及大分子，超分子和纳米化学）以及数学科学部（应用数学计划）。