This is an interdisciplinary program at the interface of mathematics, quantum semiconductor physics, and the material science of GaN semiconductors, devoted to the rigorous understanding and control of the disordered systems with the aim to grant the power to design, beyond just observing, new quantum objects hidden in disordered semiconductor materials. A program of theoretical and experimental research will be launched which pioneers the use of localized states in disordered semiconductor alloys as quantum dots and offers breakthrough achievements across several related areas which range from mathematics of the disordered systems, to quantum physics, to nanoscale materials design and characterization. The grand goal of this project is to predict and manipulate localization properties of electron matter waves in disordered media in precise, quantifiable, mathematical terms, with the applications to novel well-behaved quantum objects in the localization regions of semiconductor alloys.
Specifically, in mathematics, the project aims at the first deterministic theory revealing the precise geometric structure of waves and more general solutions to PDEs in the presence of disorder. The first treatment of localization in Poisson-Schrodinger and similar self-consistent systems, and the first treatment of localization by geometry, and a complete resolution of the problem of absolute continuity of elliptic measure. In experimental material science, the project aims at the inauguration of the field of localization engineering, including designing self-occurring nanostructures, based on the InGaN materials system of LEDs, with desired properties based on the control of electron localization at the microscopic scale, optimization of their exciton properties, control of the transport between the localized states, their relaxation and coherence times. In physics, the goal is a new approach to quantum effects in disordered systems, with the emphasis on the outstanding open problems of decoherence in quantized semiconductor structures. At stake is the demonstration that disorder can greatly improve quantum parameters such as the coherence time, which is the first mandatory step for building stable entangled state generators.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
