Small scale quantum ergodicity in negatively curved manifolds

Xiaolong Han

doi:10.1088/0951-7715/28/9/3263

Small scale quantum ergodicity in negatively curved manifolds

Xiaolong Han^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

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 h → 0. The rate of shrinking is a power. This extends the asymptotic equidistribution of quantum ergodic eigenfunctions to a logarithmical scale.

Original language	English
Pages (from-to)	3263-3288
Number of pages	26
Journal	Nonlinearity
Volume	28
Issue number	9
DOIs	https://doi.org/10.1088/0951-7715/28/9/3263
Publication status	Published - 1 Sept 2015

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title = "Small scale quantum ergodicity in negatively curved manifolds",

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 h → 0. The rate of shrinking is a power. This extends the asymptotic equidistribution of quantum ergodic eigenfunctions to a logarithmical scale.",

keywords = "asymptotic equidistribution of eigenfunctions, exponential decay of correlation, negatively curved manifolds, quantum ergodicity in small scales",

author = "Xiaolong Han",

note = "Publisher Copyright: {\textcopyright} 2015 IOP Publishing Ltd & London Mathematical Society.",

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AB - 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 h → 0. The rate of shrinking is a power. This extends the asymptotic equidistribution of quantum ergodic eigenfunctions to a logarithmical scale.

KW - asymptotic equidistribution of eigenfunctions

KW - exponential decay of correlation

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KW - quantum ergodicity in small scales

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EP - 3288

JO - Nonlinearity

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Small scale quantum ergodicity in negatively curved manifolds

Abstract

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