Transport in Quantum Systems

This award will fund research on disordered quantum matter, an interdisciplinary research area interlinking physics, computer science, and mathematics. Disorder is an inherited feature of any physical system, but the miniaturization of physical devices makes them especially sensitive to noise and imperfections. A longstanding goal of this project is to understand the behavior of materials that could play a crucial role in creating quantum computers robust to defects and noise. The principal investigator will develop an underlying mathematical theory that will allow for a better understanding of the properties of such materials, shed light on how to manipulate them more effectively, and harness disorder to enhance the stability of the desired outcomes. Progress in understanding the behavior of such systems will increase the scientific community's understanding of models in theoretical physics and applied mathematics. Students involved in this project will work alongside the PI and gain expertise in the area. The project will proceed through a program to build a self-contained, systematic transport theory in the many-body, disordered framework. The first goal of this project is to make substantial progress in understanding the time evolution of such systems, particularly the many-body localization phenomenon and its robustness to (time-dependent) perturbations. This step requires understanding the quasi-locality properties associated with this framework, which have so far been obtained only in the context of the gapped ground states associated with local Hamiltonians. The project's second goal is the analysis of the transport properties of disordered many-body Hamiltonians, particularly spin systems. It relies on constructing a many-body index theory that remains stable in a mobility gap region of the associated system and on the justification of Kubo's transport formulae for the linear response. 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.