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標題Title: APPLICATIONS OF SMALL SCALE QUANTUM ERGODICITY IN NODAL SETS
作者Authors: HAMID HEZARI AND GABRIEL RIVIERE
上傳單位Department: 電子工程系
上傳時間Date: 2016-6-8
上傳者Author: 傅俊結
審核單位Department: 電子工程系
審核老師Teacher: 傅俊結
檔案類型Categories: 論文Thesis
關鍵詞Keyword: quantum ergodicity
摘要Abstract: The goal of this article is to draw new applications of small scale quantum ergodicity in nodal sets of eigenfunctions. We show that if quantum ergodicity holds on balls of shrinking radius r(λ) → 0 then one can achieve improvements on the recent upper bounds of Logunov [Lo16a] and Logunov-Malinnikova [LoMa16] on the size of nodal sets, according to a certain power of r(λ). We also show that the order of vanishing results of Donnelly-Fefferman [DoFe88, DoFe90] and Dong [Do92] can be improved. Since by [Han15, HeRi16] small scale QE holds on negatively curved manifolds at logarithmically shrinking rates, we get logarithmic improvements on such manifolds for the above measurements of eigenfunctions. We also get o(1) improvements for manifolds with ergodic geodesic flows. Our results work for a full density subsequence of any given orthonormal basis of eigenfunctions.

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2016_6_f8498b79.pdf 265Kb pdf 32 --
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