7 citations · 29 across the 17 of their papers we have counts for
18 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…
Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap
Simon Becker, Mengxuan Yang
We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentiall…
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…
Strichartz estimates for Schrödinger equations with the multipole Aharonov--Bohm Hamiltonian
Mengxuan Yang, Junyong Zhang
We prove global-in-time Strichartz estimates for Schrödinger equations with multipole Aharonov--Bohm Hamiltonians on . As intermediate steps, we prove global-in-time…
Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces
Ziang Chen, Liqiang Huang, Mengxuan Yang +1
We establish a regularity theorem for second-order elliptic PDEs on in spectral Barron spaces. Under mild ellipticity and smallness assumptions, the solution gains…
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…
From resolvent expansions at zero to long time wave expansions
T. J. Christiansen, K. Datchev, M. Yang
We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundednes…
Low energy resolvent asymptotics of the multipole Aharonov--Bohm Hamiltonian
T. J. Christiansen, K. Datchev, M. Yang
We compute low energy asymptotics for the resolvent of the Aharonov--Bohm Hamiltonian with multiple poles for both integer and non-integer total fluxes. For integral total flux we…
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,…
Twisted TMDs in the small-angle limit: exponentially flat and trivial bands
Simon Becker, Mengxuan Yang
Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe [C23,Z23] and WSe [MD23]. In this article, we study the MacDo…
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…
The Morse index theorem for mechanical systems with reflections
Jared Wunsch, Mengxuan Yang, Yuzhou Zou
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed a…
Flat Bands and High Chern Numbers in Twisted Multilayer Graphene
Mengxuan Yang
Motivated by recent Physical Review Letters of Wang-Liu and Ledwith-Vishwanath-Khalaf, we study Tarnopolsky-Kruchkov-Vishwanath chiral model of two sheets of -layer Bernal stack…
Resolvent estimates for the magnetic Hamiltonian with singular vector potentials and applications
Mengxuan Yang
For the magnetic Hamiltonian with singular vector potentials, we analytically continue the resolvent to a logarithmic neighborhood of the positive real axis and prove resolvent est…
The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials
Mengxuan Yang
We study leading order singularities of the wave trace of the Aharonov--Bohm Hamiltonian on with multiple solenoids under a generic assumption that no three solenoid…
New counterexamples to Strichartz estimates for the wave equation on a 2d model convex domain
Oana Ivanovici, Gilles Lebeau, Fabrice Planchon
We prove that the range of Strichartz estimates on a model 2D convex domain may be further restricted compared to the known counterexamples due to the first author. Our new family…
Propagation of polyhomogeneity, Diffraction and Scattering on Product Cones
Mengxuan Yang
We consider diffraction of waves on a product cone. We first show that diffractive waves enjoy a one-step polyhomogeneous asymptotic expansion, which is an improvement of Cheeger-T…
Scattering resonances on truncated cones
Dean Baskin, Mengxuan Yang
We consider the problem of finding the resonances of the Laplacian on truncated Riemannian cones. In a similar fashion to Cheeger--Taylor, we construct the resolvent and scattering…