Riemann moduli spaces are quantum ergodic

2019/08/19 by Baskin, Dean, Gell-Redman, Jesse, Han, Xiaolong
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1908.06949

Abstract

In this note we show that the Riemann moduli spaces M_{g, n} equipped with the Weil--Petersson metric are quantum ergodic for 3g+n ≥ 4. We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.

Related

• Remarks on quantum ergodicity
• Quantum ergodicity for pseudo-Laplacians
• Quantum Ergodicity and the Analysis of Semiclassical Pseudodifferential Operators
• Quantum ergodicity for contact metric structures
• Ergodic properties of the quantum geodesic flow on tori