CONCENTRATION OF BLOCH EIGENSTATES IN THE PRESENCE OF GAUGE AT THE SEMI-CLASSICAL LIMIT

作     者：Gershon Wolansky Gershon Wolansky Department of Mathematics, Technion, Haifa 32000, Israel

作者机构：Department of Mathematics 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2011年第31卷第6期

页      面：2278-2284页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 

基　　金：supported by the Israel Science Foundation 

主　　题：SchrSdinger equation gauge semi classical limit Bloch eigenstate 

摘      要：We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge, In the semi-classical limit h → 0 these eigenstates concentrate near a maximizer of the scalar potential of the associated Schr6dinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.