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

Access to Document

10.1088/0951-7715/28/9/3263

Cite this

@article{72a132686af14818a03115df95fd2474,

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.",

year = "2015",

month = sep,

day = "1",

doi = "10.1088/0951-7715/28/9/3263",

language = "English",

volume = "28",

pages = "3263--3288",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "9",

}

TY - JOUR

T1 - Small scale quantum ergodicity in negatively curved manifolds

AU - Han, Xiaolong

PY - 2015/9/1

Y1 - 2015/9/1

N2 - 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.

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

KW - negatively curved manifolds

KW - quantum ergodicity in small scales

UR - https://www.scopus.com/pages/publications/84940100273

U2 - 10.1088/0951-7715/28/9/3263

DO - 10.1088/0951-7715/28/9/3263

M3 - Article

SN - 0951-7715

VL - 28

SP - 3263

EP - 3288

JO - Nonlinearity

JF - Nonlinearity

IS - 9

ER -

Small scale quantum ergodicity in negatively curved manifolds

Abstract

Access to Document

Other files and links

Fingerprint

Cite this