Delocalization of Schrödinger eigenfunctions - Nalini Anantharaman (France)——ICM2018的一小时报告
发文时间：2018-09-28
来源：304am永利集团
Abstract: A hundred years ago, Einstein wondered about quantization conditions for classically ergodic systems. Although a mathematical description of the spectrum of Schrödinger operators associated to ergodic classical dynamics is still completely missing, a lot of progress has been made on the delocalization of the associated eigenfunctions
https://eta.impa.br/dl/PL013.pdf
本文讨论Laplace算子的特征函数的遍历性质。首先研究关于紧Riemann流形的量子遍历性定理和量子唯一遍历性猜想，然后再考虑非紧流形上的类似问题。作者还研究了正则图上的Laplace算子的特征函数的分布问题，如：量子遍历性。最后讨论随机正则图的量子唯一遍历性，算术量子遍历性和高亏格Riemann曲面上的量子遍历性。
相关附件
14-PL013 Anantharaman
