1 citations · 2 across the 12 of their papers we have counts for
14 papers
On optimal Wannier decay in dimension three
Simon Becker, Zhongkai Tao, Mengxuan Yang
For a Chern nontrivial Bloch bundle over the three torus, we construct an orthonormal Wannier basis with the optimal pointwise decay . All but one of the g…
Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
Zhongkai Tao, Mengxuan Yang
For periodic Schrödinger operators with bounded real-valued potentials on with , we show that for generic potentials, each endpoint of every spectra…
Generic twisted Pollicott--Ruelle resonances and zeta function at zero
Tristan Humbert, Zhongkai Tao
For a connected orientable closed surface of genus with Anosov geodesic flow, we show the existence of an open subset of finite-dimensional irreducible representa…
Polynomial bounds for eigenfunctions and eigenvalues on random covers of hyperbolic surfaces
Elena Kim, Zhongkai Tao
Let be a compact connected orientable hyperbolic surface and let be a degree cover, taken uniformly at random. We show that, with high probability, the nor…
Integral formulas for under/overdetermined differential operators via recovery on curves and the finite-dimensional cokernel condition I: General theory
Philip Isett, Yuchen Mao, Sung-Jin Oh +1
We introduce a new versatile method for constructing solution operators (i.e., right-inverses up to a finite rank operator) for a wide class of underdetermined PDEs , whic…
Wannier decay and the Thouless conjecture
Simon Becker, Zhongkai Tao, Mengxuan Yang
Non-trivial Chern classes pose an obstruction to the existence of exponentially decaying Wannier functions which provide natural bases for spectral subspaces. For non-trivial Bloch…
Lossless Strichartz and spectral projection estimates on unbounded manifolds
Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao +1
We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order…
Fragile topology on solid grounds: a mathematical perspective
Simon Becker, Zhongkai Tao, Mengxuan Yang
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension , vanishing Chern classes of bundles of Bloch eigen…
Selberg, Ihara and Berkovich
Jialun Li, Carlos Matheus, Wenyu Pan +1
We use the Selberg zeta function to study the limit behavior of resonances in a degenerating family of Kleinian Schottky groups. We prove that, after a suitable rescaling, the Selb…
Dirac cones and magic angles in the Bistritzer--MacDonald TBG Hamiltonian
Simon Becker, Solomon Quinn, Zhongkai Tao +2
We demonstrate the generic existence of Dirac cones in the full Bistritzer--MacDonald Hamiltonian for twisted bilayer graphene. Its complementary set, when Dirac cones are absent,…
Spectral gap for surfaces of infinite volume with negative curvature
Zhongkai Tao
We prove that the imaginary parts of scattering resonances for negatively curved asymptotically hyperbolic surfaces are uniformly bounded away from zero and provide a resolvent bou…
Mathematical results on the chiral model of twisted bilayer graphene (with an appendix by Mengxuan Yang and Zhongkai Tao)
Maciej Zworski, Mengxuan Yang, Zhongkai Tao
The study of twisted bilayer graphene (TBG) is a hot topic in condensed matter physics with special focus on {\em magic angles} of twisting at which TBG acquires unusual properties…
Optimal enhanced dissipation for contact Anosov flows
Zhongkai Tao, Maciej Zworski
We show that for a contact Anosov flow on a compact manifold , the solutions to , , where is the generator of the flow and , a (n…
Classically forbidden regions in the chiral model of twisted bilayer graphene. With an appendix by Zhongkai Tao and Maciej Zworski
Michael Hitrik, Zhongkai Tao, Maciej Zworski
We establish exponential decay, as the angle of twisting goes to , of eigenstates in a model of twisted bilayer graphene (TBG), near the hexagon connecting stacking points. Tha…