7 papers
A Gutzwiller trace formula for singular potentials
Jared Wunsch, Mengxuan Yang, Yuzhou Joey Zou
The Gutzwiller trace formula relates the asymptotic spacing of quantum-mechanical energy levels in the semiclassical limit to the dynamics of periodic classical particle trajectori…
Logarithmic wave decay for short range wavespeed perturbations with radial regularity
Gayana Jayasinghe, Katrina Morgan, Jacob Shapiro +1
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbatio…
On the dichotomy of -walk dimensions on metric measure spaces
Meng Yang
On a volume doubling metric measure space endowed with a family of -energies such that the Poincaré inequality and the cutoff Sobolev inequality with -walk dimension ho…
Flat bands, Dirac cones, and higher-order band crossings in twisted multilayer graphene
Bryan Li, Mengxuan Yang
For the chiral limit of two sheets of -layer Bernal-stacked graphene established in the Physical Review Letters arXiv:2109.10325 and arXiv:2109.11514, we prove a trichotomy: dep…
Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees
Fabrice Baudoin, Li Chen, Meng Yang
We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform vo…
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…