Gap Control by Singular Schr?dinger Operators in a Periodically Structured Metamaterial

Pavel Exner; Andrii Khrabustovskyi

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Gap Control by Singular Schr?dinger Operators in a Periodically Structured Metamaterial

机译：周期结构超材料中奇异薛定ding算子的间隙控制

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We consider a family fH"g"0 of "Zn-periodic Schr¨odinger operators with 0-interactions supported on a lattice of closed compact surfaces; within aminimum period cell one has m 2 N surfaces. We show that in the limitwhen " ! 0 and the interactions strengths are appropriately scaled, H" hasat most m gaps within finite intervals, and moreover, the limiting behaviorof the first m gaps can be completely controlled through a suitable choice ofthose surfaces and of the interactions strengths.

机译：我们考虑一个“ f-H” g“> 0族，其“ Zn周期Schrodinger算子具有0个相互作用，并支持在一个封闭的紧致表面的晶格上;在最小周期内，一个单元具有m 2 N个表面。我们证明，当” ！ 0和强度被适当地缩放的相互作用，有限的时间间隔内H” hasat最m个间隙，而且，behaviorof第一米间隙限制可以完全通过一个合适的选择ofthose表面和相互作用强度的控制。

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《Journal of Mathematical Physics, Analysis, Geometry》 |2018年第3期|共16页
作者
Pavel Exner; Andrii Khrabustovskyi;
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中图分类高等数学;
关键词
periodic Schr¨odinger operators0 interactionspectral gapseigenvalue asymptotics;

机译：周期Schr？odinger算子0相互作用谱间隙特征值渐近性;

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1. Spectral gaps of Schr?dinger operators with periodic singular potentials [J] . Plamen Djakov, Boris Mityagin Dynamics of partial differential equations . 2009,第2期

机译：具有周期奇异势的薛定er算子的谱隙
2. SPECTRAL GAPS OF THE ONE-DIMENSIONAL SCHR_DINGER OPERATORS WITH SINGULAR PERIODIC POTENTIALS [J] . VLADIMIR MIKHAILETS, VOLODYMYR MOLYBOGA Methods of Functional Analysis and Topology . 2009,第1期

机译：一维奇异周期势的Schr_dinger算子的谱隙
3. Spectral gap asymptotics of one-dimensional Schr_dinger operators with singular periodic potentials [J] . P. Djakov, B. Mityagin Integral transforms and special functions . 2009,第3a4期

机译：具有奇异周期势的一维Schr_dinger算子的谱隙渐近性
4. Complex powers of the Schr?dinger operator with singular potential [C] . Alimdjan Khalmukhamedov USA-Uzbekistan Conference on Analysis and Mathematical Physics . 2016

机译：SCHR的复杂力量倾向于奇异潜力
5. Semigroups for One-Dimensional Schr?dinger Operators with Multiplicative Gaussian Noise [D] . Gaudreau Lamarre, Pierre Yves. 2020

机译：半群的一维SCHR？Dinger运算符，具有乘法高斯噪声
6. Commutators associated with Schrödinger operators on the nilpotent Lie group [O] . Tianzhen Ni, Yu Liu -1

机译：与幂零李群上的薛定ding算子相关的换向器
7. Spectral gaps of Schrödinger operators with periodic singular potentials [O] . Plamen Djakov, Boris Mityagin 2012

机译：具有周期奇异势的薛定谔算子的谱空间

Gap Control by Singular Schr?dinger Operators in a Periodically Structured Metamaterial

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