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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
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).
キーワード
Periodic Schrödinger operator
oscillating potential
spectral shift function
asymptotic expansions
resonances
発行日
2017-01
出版物タイトル
Mathematical Journal of Okayama University
59巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
開始ページ
149
終了ページ
174
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
オフィシャル URL
http://www.math.okayama-u.ac.jp/mjou/
言語
English
著作権者
Copyright©2017 by the Editorial Board of Mathematical Journal of Okayama University
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol59/iss1/12