McKnight Presidential Professor Douglas Arnold

CSENG Mathematics, School of
College of Science & Engineering
Twin Cities
Project Title: 
Computational Study of Eigenvalue Localization and Numerical Relativity

These researchers continue to work as part of an interdisciplinary group of mathematicians and physicists on understanding Anderson localization, or, more generally, the localization of eigenfunctions of elliptic operators by disorder. This phenomenon, which is of great significance in many applications (such as quantum mechanics where it gives rise to a metal/insulator transition in disordered alloys), is famously difficult to explain, predict, and control. This group's approach is based on a new technology called the landscape function. Algorithms based on the landscape function are able to predict the spectrum of Schrodinger operators with disorded potentials accurately without the need to solve any eigenvalue problems. These approaches are rapidly becoming a go-to tool in semiconductor modeling and related areas, and have already contributed to major increases in the efficiency of green LEDs, of great significance for electrical energy consumption.

Project Investigators

McKnight Presidential Professor Douglas Arnold
Chuning Wang
Qile Yan
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