# A Dynamical Theory of Floquet Materials

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · New Jersey Institute of Technology (NJ) · $182,956

## Abstract

This project investigates Floquet materials—engineered systems whose properties are dynamically altered using time-periodic forcing, such as shining light on graphene or modulating optical waveguides. This approach allows for reversible control of physical behavior and has gained traction in fields like quantum engineering, photonics, and acoustics. Although experimental studies have observed intriguing phenomena like edge conduction in these materials, the theoretical foundation—especially in continuum models described by partial differential equations—is incomplete and, at times, contradictory. The investigator develops a rigorous mathematical framework for understanding Floquet materials using continuum models, with the goal of explaining fundamental features such as wave localization and energy transport. The project serves the national interest by advancing foundational science in applied mathematics and mathematical physics, and contributing to emerging technologies that rely on wave manipulation. The project supports graduate education at the New Jersey Institute of Technology and promotes collaboration and dissemination of scientific knowledge through scientific workshops and seminars.

The investigator studies time-periodic parametric forcing in periodic media, focusing on non-autonomous dispersive partial differential equations (PDE) — specifically Schrodinger and Dirac equations—in contrast to the prevalent use of discrete, tight-binding approximations. The proje

## Key facts

- **NSF award ID:** 2508811
- **Awardee organization:** New Jersey Institute of Technology (NJ)
- **SAM.gov UEI:** SGBMHQ7VXNH5
- **PI:** Amir Sagiv
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $182,956
- **Funds obligated:** $182,956
- **Transaction type:** Standard Grant
- **Period:** 09/01/2025 → 08/31/2027

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2508811

## Citation

> US National Science Foundation, Award 2508811, A Dynamical Theory of Floquet Materials. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2508811. Licensed CC0.

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