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Research Spending & Results

Award Detail

Doing Business As Name:Louisiana State University
  • Rui Han
  • (949) 878-8453
Award Date:09/14/2020
Estimated Total Award Amount: $ 51,713
Funds Obligated to Date: $ 51,713
  • FY 2018=$51,713
Start Date:08/13/2020
End Date:07/31/2021
Transaction Type:Grant
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Discrete Schrodinger Operators and Related Models
Federal Award ID Number:2053285
DUNS ID:075050765
Parent DUNS ID:940050792
Program Officer:
  • Marian Bocea
  • (703) 292-2595

Awardee Location

Street:202 Himes Hall
City:Baton Rouge
County:Baton Rouge
Awardee Cong. District:06

Primary Place of Performance

Organization Name:Louisiana State University
City:Baton Rouge
County:Baton Rouge
Cong. District:06

Abstract at Time of Award

This project concerns the spectral theory of Schrodinger operators, a central topic in quantum mechanics. Schrodinger operators describe the movement of an electron in a medium subject to a disordered system. The development of the theory of Schrodinger operators is expected to enhance the understanding of many types of physical phenomena, including conductance, quantum Hall effect, quasicrystals, and graphene. The PI intends to develop new tools to provide rigorous mathematical explanations for these phenomena. The tools that will be developed will also find applications in other branches of mathematics, including harmonic analysis, probability and number theory. This project consists of several parts. One is to study quantum graphs in magnetic fields. The PI intends to understand the topological structure of the spectrum and spectral decompositions. The second part involves studying Laplacians on discrete periodic graphs with a goal of finding the connection between the presence of spectral gaps and the geometric structure of the underlying lattice. The third goal concerns discrete quasi-periodic Schrodinger operators, focusing on several well-known problems including measure of the spectrum, continuity of the spectrum, structure of eigenfunctions in the localization regime and quantum dynamics in the singular continuous regime for quasi-periodic operators. Another goal is to understand Schrodinger operators with potentials generated by skew-shift. These operators, although being completely deterministic, are expected to resemble random features. 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.

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