Small scale quantum ergodicity in negatively curved manifolds

Xiaolong Han

Type: Article

Publication Date: 2015-08-13

Citations: 37

DOI: https://doi.org/10.1088/0951-7715/28/9/3263

Abstract

In this paper, we investigate quantum ergodicity in negatively curved manifolds. We consider the symbols depending on a semiclassical parameter h with support shrinking down to a point as . The rate of shrinking is a power of . This extends the asymptotic equidistribution of quantum ergodic eigenfunctions to a logarithmical scale.

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