Publications

Pre-prints and Publications

1. Mathematical foundations of phonons in incommensurate materials (with M. Hott, M. Luskin) [preprint] 

2. Construction and accuracy of electronic continuum models of incommensurate bilayer 2D materials (with X. Quan, D. Massatt) [preprint] 

3. Ergodic properties of one-dimensional incommensurate bilayer materials (with N. J. Essner) [preprint]

4. Dirac cones and magic angles in the Bistritzer-MacDonald TBG Hamiltonian (with S. Becker, S. Quinn, Z. Tao, M. Yang); submitted [preprint]

5. Learning the local density of states of a bilayer moiré material in one dimension (with D. Liu, S. Carr, M. Luskin); submitted [preprint]

6. Radiative transport in a periodic structure with band crossings (with K. Qi, L. Wang); SIAM Journal on Applied Mathematics (2024)  [preprint]

7. From incommensurate bilayer heterostructures to Allen-Cahn: An exact thermodynamic limit (with M. Hott, M. Luskin); Archive for Rational Mechanics and Analysis 248 103 (2024) [article, preprint]

8. Modeling of electronic dynamics in twisted bilayer graphene (with T. Kong, D. Liu, M. Luskin); SIAM Journal on Applied Mathematics 84 3 1011-1038 (2024) [article, preprint]

9. Locality of the windowed local density of states (with T. A. Loring, J. Lu);  Numerische Mathematik 156 741-775 (2024) [article, preprint]

10. Mathematical aspects of the Kubo formula for electrical conductivity with dissipation (with D. Margetis, M. Luskin); Japan Journal of Industrial and Applied Mathematics 40 1765-1795 (2023) [article, preprint]

11. Edge state dynamics along curved interfaces (with G. Bal, S. Becker, A. Drouot, C. Fermanian-Kammerer, J. Lu); SIAM Journal on Mathematical Analysis 55 5 4219-4254 (2023) [article, preprint]

12. On the Su-Schrieffer-Heeger model of electron transport: low-temperature optical conductivity by the Mellin transform (with D. Margetis, M. Luskin); Studies in Applied Mathematics 151 555-584 (2023) [article, preprint]

13. Bistritzer-MacDonald dynamics in twisted bilayer graphene (with T. Kong, A. H. MacDonald, M. Luskin); Journal of Mathematical Physics 64 031502 Editor's Pick (2023) [article, preprint]

14. Computing spectral properties of topological insulators without artificial truncation or supercell approximation (with M. J. Colbrook, A. Horning, K. Thicke); IMA Journal of Mathematics 88 1 1-42 (2023) [article, preprint]

15. Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher (with K. D. Stubbs, J. Lu); Archive for Rational Mechanics and Analysis 243 3 (2022) [article, preprint]

16. Defect state resonances of truncated crystal structures (with J. Lu and J. Marzuola); SIAM Journal on Applied Mathematics 82 1 (2022) [article, preprint]

17. Existence of the first magic angle for the chiral model of bilayer graphene (with M. Luskin); Journal of Mathematical Physics 62 091502 (2021) [article, preprint]

18. Wave-packet propagation in a finite topological insulator and the spectral localizer index (with J. Michala, A. Pierson, T. Loring); Involve 14 2 209-239 (2021) [article, preprint]

19. Computing edge states without hard truncation (with K. Thicke, J. Lu); SIAM Journal on Scientific Computing 43 2 B323-B353 (2021) [article, preprint]

20. The Iterated Projected Position algorithm for constructing exponentially localized generalized Wannier functions for periodic and non-periodic insulators in two dimensions and higher (with K. D. Stubbs, J. Lu); Physical Review B 103 075125 (2021) [article, preprint]

21. Dirac operators and domain walls (with J. Lu, M. I. Weinstein); SIAM Journal on Mathematical Analysis 52 2 1115-1145 (2020) [article, preprint]

22. Wavepackets in inhomogeneous periodic media: Propagation through a one-dimensional band crossing (with M. I. Weinstein); Communications in Mathematical Physics 363 655-698 (2018) [article, preprint]

23. Wavepackets in inhomogeneous periodic media: Effective particle-field dynamics and Berry curvature (with J. Lu, M. I. Weinstein); Journal of Mathematical Physics 58 021503 (2017) [article, preprint]

Thesis

Wave dynamics in locally periodic structures by multiscale analysis Columbia (APAM) PhD thesis, supervised by M. I. Weinstein (2017) [pdf]