Roman Shterenberg
University of Alabama at Birmingham, AL·Mathematics & Statistics
Most crystals are built from patterns that repeat exactly, like tiles on a floor. Some materials, however, are highly ordered without ever repeating.
- Fields
Mathematics & Statistics
Physics
- Topics
almost-periodic operators
quasi-periodic operators
quasicrystals
- Grants
- 1 known grant, through May 2027
What they work on
- Analyze mathematical models of almost-periodic operators from quantum mechanics to explain the mechanism of electrical conductivity in modulated, non-repeating crystals.
- Investigate the metal-insulator transition, in which a material switches between conducting and blocking current, in quasi-periodic structures using asymptotic analysis.
- Combine tools from partial differential equations and complex analysis to address open questions in spectral theory, spectral geometry, quantum networks and photonic crystals.
More about the research
These aperiodic crystals and quasicrystals turn up in metal alloys, minerals, organic compounds and even some proteins. Understanding how electrons move through such structures is a basic question in solid-state physics. This project studies it using the mathematics of quantum mechanics.
Why it matters
This is basic mathematical research. It aims to provide a rigorous understanding of how electrons behave in aperiodic crystals and quasicrystals, including the switch between metallic and insulating behavior. Such results could eventually help explain or predict experimental observations in materials physics and photonic crystals. The improved methods may also apply to other problems in mathematics and physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Svetlana Jitomirskaya
University of California-Berkeley, CA·Mathematics & Statistics
Develop non-perturbative Green's function estimates for lattice quasiperiodic operators when the frequency parameter is restricted to a submanifold of a torus.
Wei Li
DePaul University, IL·Mathematics & Statistics
Prove the existence of and characterize edge states, the waves that travel along a boundary, on sharp interfaces formed by joining photonic materials with various symmetries, within a partial differential equation framework.
Yan Wang
University of Nevada-Reno, NV·Engineering·Early-career
Determine how wave-like phonons, atomic vibrations that carry heat, travel, scatter and become trapped in periodic, quasi-periodic and aperiodic structures, combining spectral phonon analysis with phonon spectroscopy.
The school
University of Alabama at Birmingham: 45 labs on PI Pages, $866M a year on research, 166 research doctorates a year.
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