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math.AP2020
Small scale quantum ergodicity in cat maps. II. Quasimodes that are not equidistributed at the logarithmical scales
Xiaolong Han
In this series, we investigate quantum ergodicity at small scales for linear hyperbolic maps of the torus ("cat maps'"). In Part II of the series, we construct quasimodes that are…
math.AP2019
Riemann moduli spaces are quantum ergodic
Dean Baskin, Jesse Gell-Redman, Xiaolong Han
In this note we show that the Riemann moduli spaces equipped with the Weil--Petersson metric are quantum ergodic for . We also provide other examples of sin…
math.AP2017★ 1 cited
Nodal lengths of eigenfunctions in the disc
Xiaolong Han, Michael Murray, Chuong Tran
In this paper, we derive the sharp lower and upper bounds of nodal lengths of Laplacian eigenfunctions in the disc. Furthermore, we observe a geometric property of the eigenfunctio…