EAGER: Quantum Nanosystems Understood the Multiscale Way

Indiana University, Bloomington IN

Investigators

Abstract

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).