ID | 54721 |
フルテキストURL | |
著者 |
Dimassi, Mouez
Universit´e Bordeaux I, Institut de Math´ematiques de Bordeaux
Anh Tuan Duong
Department of Mathematics, Hanoi National University of Education
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抄録 | In the semi-classical regime (i.e., h ↘ 0), we study the effect of an oscillating decaying potential V (hy, y) on the periodic Schrödinger operator H. The potential V (x, y) is assumed to be smooth, periodic with respect to y and tends to zero as |x| → ∞. We prove the existence of O(h−n) eigenvalues in each gap of the operator H + V (hy, y). We also establish a Weyl type asymptotics formula of the counting function of eigenvalues with optimal remainder estimate. We give a weak and pointwise asymptotic expansions in powers of h of the spectral shift function corresponding to the pair (H + V (hy, y),H). Finally, under some analytic assumption on the potential V we prove the existence of shape resonances, and we give their asymptotic expansions in powers of h1/2. All our results depend on the Floquet eigenvalues corresponding to the periodic Schrödinger operator H +V (x, y), (here x is a parameter).
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キーワード | Periodic Schrödinger operator
oscillating potential
spectral shift function
asymptotic expansions
resonances
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発行日 | 2017-01
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出版物タイトル |
Mathematical Journal of Okayama University
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巻 | 59巻
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号 | 1号
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出版者 | Department of Mathematics, Faculty of Science, Okayama University
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開始ページ | 149
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終了ページ | 174
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ISSN | 0030-1566
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NCID | AA00723502
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資料タイプ |
学術雑誌論文
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オフィシャル URL | http://www.math.okayama-u.ac.jp/mjou/
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言語 |
英語
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著作権者 | Copyright©2017 by the Editorial Board of Mathematical Journal of Okayama University
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論文のバージョン | publisher
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査読 |
有り
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Submission Path | mjou/vol59/iss1/12
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JaLCDOI |