Universal hierarchical structure of quasiperiodic eigenfunctions S Jitomirskaya, W Liu Annals of Mathematics 187 (3), 721-776, 2018 | 102 | 2018 |
Arithmetic spectral transitions for the Maryland model S Jitomirskaya, W Liu Communications on Pure and Applied Mathematics 70 (6), 1025-1051, 2017 | 64 | 2017 |
Anderson localization for multi-frequency quasi-periodic operators on S Jitomirskaya, W Liu, Y Shi Geometric and Functional Analysis 30 (2), 457-481, 2020 | 44 | 2020 |
Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase S Jitomirskaya, W Liu arXiv preprint arXiv:1802.00781, 2018 | 44 | 2018 |
Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues W Liu Geometric and Functional Analysis 32 (1), 1-30, 2022 | 31 | 2022 |
Quantitative inductive estimates for Green’s functions of non-self-adjoint matrices W Liu Analysis & PDE 15 (8), 2061-2108, 2023 | 27 | 2023 |
Irreducibility of the Bloch variety for finite-range Schrödinger operators J Fillman, W Liu, R Matos Journal of Functional Analysis 283 (10), 109670, 2022 | 27 | 2022 |
Criteria for embedded eigenvalues for discrete Schrödinger operators W Liu International Mathematics Research Notices 2021 (20), 15803-15832, 2021 | 23 | 2021 |
Anderson localization for the almost Mathieu operator in the exponential regime W Liu, X Yuan Journal of Spectral Theory 5 (1), 89-112, 2015 | 18 | 2015 |
Spectral gaps of almost Mathieu operators in the exponential regime W Liu, X Yuan Journal of Fractal Geometry 2 (1), 1-51, 2015 | 18 | 2015 |
Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators W Liu, DC Ong Journal d'Analyse Mathématique 141 (2), 625-661, 2020 | 17 | 2020 |
Fermi isospectrality for discrete periodic Schrödinger operators W Liu Communications on Pure and Applied Mathematics 77 (2), 1126-1146, 2024 | 16 | 2024 |
Impacts of Yongding River on the Xishan karst aquifer and Yuquan spring in Beijing, China D QIN, J SUN, Y GUO, L LI, H MUHAMMED, D WANG, W LIU Journal of Engineering Geology 27 (1), 162-169, 2019 | 16 | 2019 |
Topics on Fermi varieties of discrete periodic Schrödinger operators W Liu Journal of Mathematical Physics 63 (2), 2022 | 15 | 2022 |
Effect of Yufu river on chemical process of karst groundwater in Ji'nan, Shandong province B LI, D QIN, Y GUO, W LIU, H Mohammed, LIN Lin, Q GUAN Journal of Engineering Geology 25 (1), 190-198, 2017 | 15 | 2017 |
Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies W Liu, Y Shi Journal of Spectral Theory 9 (4), 1223-1248, 2019 | 14 | 2019 |
Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian S Jitomirskaya, W Liu Geometric and Functional Analysis 29, 238-257, 2019 | 14 | 2019 |
Anderson localization for the completely resonant phases W Liu, X Yuan Journal of Functional Analysis 268 (3), 732-747, 2015 | 14 | 2015 |
Universal reflective-hierarchical structure of quasiperiodic eigenfunctions and sharp spectral transition in phase S Jitomirskaya, W Liu Journal of the European Mathematical Society 26 (8), 2797-2836, 2023 | 13 | 2023 |
Upper bounds on transport exponents for long range operators S Jitomirskaya, W Liu J. Math. Phys. 62 (2021), no. 7, Paper No. 073506, 9 pp., 2021 | 13 | 2021 |